Subjects -> MATHEMATICS (Total: 1013 journals)
    - APPLIED MATHEMATICS (92 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (714 journals)
    - MATHEMATICS (GENERAL) (45 journals)
    - NUMERICAL ANALYSIS (26 journals)
    - PROBABILITIES AND MATH STATISTICS (113 journals)

MATHEMATICS (714 journals)            First | 1 2 3 4     

Showing 401 - 538 of 538 Journals sorted alphabetically
Journal of mathematical and computational science     Open Access   (Followers: 2)
Journal of Mathematical and Fundamental Sciences     Open Access  
Journal of Mathematical Behavior     Hybrid Journal   (Followers: 6)
Journal of Mathematical Chemistry     Hybrid Journal   (Followers: 5)
Journal of Mathematical Finance     Open Access   (Followers: 6)
Journal of Mathematical Imaging and Vision     Hybrid Journal   (Followers: 6)
Journal of Mathematical Logic     Hybrid Journal   (Followers: 2)
Journal of Mathematical Sciences     Hybrid Journal  
Journal of Mathematical Sciences and Applications     Open Access   (Followers: 2)
Journal of Mathematical Sociology     Hybrid Journal   (Followers: 3)
Journal of Mathematics     Open Access  
Journal of Mathematics and Statistics     Open Access   (Followers: 6)
Journal of Mathematics and Statistics Studies     Open Access  
Journal of Mathematics and the Arts     Hybrid Journal   (Followers: 1)
Journal of Mathematics Education at Teachers College     Open Access   (Followers: 5)
Journal of Mathematics in Industry     Open Access  
Journal of Mathematics Research     Open Access  
Journal of Metallurgy     Open Access   (Followers: 9)
Journal of Modern Mathematics Frontier     Open Access  
Journal of Multidisciplinary Modeling and Optimization     Open Access   (Followers: 1)
Journal of Multivariate Analysis     Hybrid Journal   (Followers: 15)
Journal of Nonlinear Analysis and Optimization : Theory & Applications     Open Access   (Followers: 4)
Journal of Nonlinear Mathematical Physics     Hybrid Journal   (Followers: 2)
Journal of Nonlinear Science     Hybrid Journal   (Followers: 1)
Journal of Numerical Cognition     Open Access   (Followers: 1)
Journal of Optimization     Open Access   (Followers: 5)
Journal of Peridynamics and Nonlocal Modeling     Hybrid Journal  
Journal of Progressive Research in Mathematics     Open Access   (Followers: 1)
Journal of Pseudo-Differential Operators and Applications     Hybrid Journal  
Journal of Pure and Applied Algebra     Full-text available via subscription   (Followers: 3)
Journal of Quantitative Linguistics     Hybrid Journal   (Followers: 6)
Journal of Scientific Computing     Hybrid Journal   (Followers: 19)
Journal of Scientific Research     Open Access  
Journal of Symbolic Computation     Hybrid Journal   (Followers: 2)
Journal of the Australian Mathematical Society     Full-text available via subscription  
Journal of the Egyptian Mathematical Society     Open Access  
Journal of the Indian Mathematical Society     Hybrid Journal  
Journal of the Institute of Mathematics of Jussieu     Hybrid Journal  
Journal of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Journal of the Nigerian Mathematical Society     Open Access  
Journal of Theoretical and Applied Physics     Open Access   (Followers: 9)
Journal of Topology and Analysis     Hybrid Journal  
Journal of Transport and Supply Chain Management     Open Access   (Followers: 10)
Journal of Turbulence     Hybrid Journal   (Followers: 7)
Journal of Universal Mathematics     Open Access  
Journal of Urban Regeneration & Renewal     Full-text available via subscription   (Followers: 8)
JRAMathEdu : Journal of Research and Advances in Mathematics Education     Open Access   (Followers: 5)
JUMLAHKU : Jurnal Matematika Ilmiah STKIP Muhammadiyah Kuningan     Open Access  
JURING (Journal for Research in Mathematics Learning)     Open Access  
Jurnal Didactical Mathematics     Open Access   (Followers: 5)
Jurnal Matematika     Open Access  
Jurnal Matematika, Sains, Dan Teknologi     Open Access  
Jurnal Natural     Open Access  
Jurnal Pendidikan Matematika Raflesia     Open Access  
Jurnal Penelitian Pembelajaran Matematika Sekolah     Open Access  
Jurnal Penelitian Sains (JPS)     Open Access  
Jurnal Riset Pendidikan Matematika     Open Access  
Jurnal Sains Matematika dan Statistika     Open Access  
Jurnal Tadris Matematika     Open Access  
Jurnal Teknologi dan Sistem Komputer     Open Access  
Kontinu : Jurnal Penelitian Didaktik Matematika     Open Access  
Kreano, Jurnal Matematika Kreatif-Inovatif     Open Access  
Le Matematiche     Open Access  
Lettera Matematica     Hybrid Journal  
Lietuvos Matematikos Rinkinys     Open Access  
Limits : Journal of Mathematics and Its Applications     Open Access  
Linear Algebra and its Applications     Full-text available via subscription   (Followers: 22)
Linear and Multilinear Algebra     Hybrid Journal   (Followers: 7)
Lithuanian Mathematical Journal     Hybrid Journal  
Lobachevskii Journal of Mathematics     Open Access  
Logic Journal of the IGPL     Hybrid Journal   (Followers: 1)
Logica Universalis     Hybrid Journal  
manuscripta mathematica     Hybrid Journal   (Followers: 1)
MaPan : Jurnal Matematika dan Pembelajaran     Open Access  
Marine Genomics     Hybrid Journal   (Followers: 1)
Matemáticas, Educación y Sociedad     Open Access  
Matematicheskie Zametki     Full-text available via subscription  
Mathematica Scandinavica     Full-text available via subscription   (Followers: 1)
Mathematical Analysis and its Contemporary Applications     Open Access   (Followers: 1)
Mathematical Communications     Open Access  
Mathematical Computation     Open Access   (Followers: 1)
Mathematical Geosciences     Hybrid Journal   (Followers: 4)
Mathematical Journal of Interdisciplinary Sciences     Open Access   (Followers: 1)
Mathematical Medicine and Biology: A Journal of the IMA     Hybrid Journal   (Followers: 1)
Mathematical Methods in the Applied Sciences     Hybrid Journal   (Followers: 3)
Mathematical Methods of Statistics     Hybrid Journal   (Followers: 4)
Mathematical Modelling and Analysis     Open Access   (Followers: 1)
Mathematical Modelling of Natural Phenomena     Open Access   (Followers: 1)
Mathematical Models and Methods in Applied Sciences     Hybrid Journal   (Followers: 1)
Mathematical Notes     Hybrid Journal  
Mathematical Proceedings of the Cambridge Philosophical Society     Full-text available via subscription   (Followers: 2)
Mathematical Programming Computation     Hybrid Journal   (Followers: 2)
Mathematical Sciences     Open Access  
Mathematical Social Sciences     Hybrid Journal   (Followers: 1)
Mathematical Theory and Modeling     Open Access   (Followers: 6)
Mathematical Thinking and Learning     Hybrid Journal   (Followers: 4)
Mathematics and Statistics     Open Access   (Followers: 2)
Mathematics Education Forum Chitwan     Open Access   (Followers: 2)
Mathematics Education Journal     Open Access   (Followers: 4)
Mathematics Education Research Journal     Partially Free   (Followers: 16)
Mathematics of Control, Signals, and Systems (MCSS)     Hybrid Journal   (Followers: 5)
Mathematics Teacher: Learning and Teaching PK-12     Full-text available via subscription   (Followers: 9)
Mathematics Teaching in the Middle School     Full-text available via subscription   (Followers: 8)
Mathematische Annalen     Hybrid Journal   (Followers: 2)
Mathematische Nachrichten     Hybrid Journal   (Followers: 1)
Mathematische Semesterberichte     Hybrid Journal  
Mathematische Zeitschrift     Hybrid Journal   (Followers: 2)
MATICS     Open Access  
Matrix Science Mathematic     Open Access   (Followers: 1)
Measurement Science Review     Open Access   (Followers: 3)
Mediterranean Journal of Mathematics     Hybrid Journal  
Memetic Computing     Hybrid Journal  
Mendel : Soft Computing Journal     Open Access  
Metaheuristics     Hybrid Journal  
Metals and Materials International     Hybrid Journal   (Followers: 1)
Metascience     Hybrid Journal   (Followers: 1)
Metrology and Instruments / Метрологія та прилади     Open Access  
Milan Journal of Mathematics     Hybrid Journal  
MLQ- Mathematical Logic Quarterly     Hybrid Journal   (Followers: 1)
Modelling in Civil and Environmental Engineering     Open Access   (Followers: 4)
MONA : Matematik- og Naturfagsdidaktik     Hybrid Journal  
Monatshefte fur Mathematik     Hybrid Journal  
Moroccan Journal of Pure and Applied Analysis     Open Access  
Moscow University Mathematics Bulletin     Hybrid Journal  
MSOR Connections     Open Access   (Followers: 1)
Multiscale Modeling and Simulation     Hybrid Journal   (Followers: 2)
MUST : Journal of Mathematics Education, Science and Technology     Open Access   (Followers: 4)
Nagoya Mathematical Journal     Hybrid Journal   (Followers: 1)
Nano Research     Hybrid Journal   (Followers: 4)
Nanotechnologies in Russia     Hybrid Journal  
Natural Resource Modeling     Hybrid Journal  
New Mathematics and Natural Computation     Hybrid Journal   (Followers: 1)
Nonlinear Analysis     Hybrid Journal   (Followers: 1)
Nonlinear Analysis : Modelling and Control     Open Access   (Followers: 1)
Nonlinear Analysis: Hybrid Systems     Hybrid Journal  
Nonlinear Analysis: Real World Applications     Hybrid Journal   (Followers: 1)
Nonlinear Differential Equations and Applications NoDEA     Hybrid Journal  
North Carolina Journal of Mathematics and Statistics     Open Access  
Note di Matematica     Open Access  
NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin     Hybrid Journal   (Followers: 3)
Numeracy : Advancing Education in Quantitative Literacy     Open Access   (Followers: 1)
Numerical Analysis and Applications     Hybrid Journal   (Followers: 1)
Numerical Functional Analysis and Optimization     Hybrid Journal   (Followers: 3)
Numerical Linear Algebra with Applications     Hybrid Journal   (Followers: 7)
Numerische Mathematik     Hybrid Journal  
Open Journal of Discrete Mathematics     Open Access   (Followers: 3)
Open Journal of Modelling and Simulation     Open Access   (Followers: 2)
Operations Research Letters     Hybrid Journal   (Followers: 11)
Optimization Letters     Hybrid Journal   (Followers: 2)
Optimization Methods and Software     Hybrid Journal   (Followers: 6)
Opuscula Mathematica     Open Access  
Order     Hybrid Journal  
ORiON     Open Access  
P-Adic Numbers, Ultrametric Analysis, and Applications     Hybrid Journal  
PAMM : Proceedings in Applied Mathematics and Mechanics     Free  
Parallel Processing Letters     Hybrid Journal   (Followers: 3)
Peking Mathematical Journal     Hybrid Journal  
Periodica Mathematica Hungarica     Full-text available via subscription   (Followers: 1)
Petroleum Science     Open Access  
Philosophia Mathematica     Hybrid Journal   (Followers: 1)
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences     Full-text available via subscription   (Followers: 9)
PNA. Revista de Investigación en Didáctica de la Matemática     Open Access  
Polar Science     Hybrid Journal   (Followers: 3)
Positivity     Hybrid Journal  
Press Start     Open Access   (Followers: 1)
Prime Number     Full-text available via subscription  
Probability in the Engineering and Informational Sciences     Hybrid Journal   (Followers: 1)
Problemy Peredachi Informatsii     Full-text available via subscription  
Proceedings - Mathematical Sciences     Open Access   (Followers: 5)
Proceedings of the American Mathematical Society, Series B     Open Access   (Followers: 4)
Proceedings of the Edinburgh Mathematical Society     Hybrid Journal  
Proceedings of the Institution of Civil Engineers - Engineering and Computational Mechanics     Hybrid Journal   (Followers: 2)
Proceedings of the Latvian Academy of Sciences. Section B: Natural, Exact and Applied Sciences     Open Access   (Followers: 1)
Proceedings of the London Mathematical Society     Hybrid Journal   (Followers: 5)
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences     Full-text available via subscription   (Followers: 6)
Proceedings of the Royal Society of Edinburgh Section A Mathematics     Full-text available via subscription  
Proceedings of the Steklov Institute of Mathematics     Hybrid Journal  
Progress in Photovoltaics: Research & Applications     Hybrid Journal   (Followers: 6)
Proyecciones : Revista de Matematica     Open Access   (Followers: 1)
Publications Mathématiques de Besançon : Algèbre et Théorie des Nombres     Open Access  
Publications Mathématiques de L'IHÉS     Hybrid Journal   (Followers: 4)
Punjab University Journal of Mathematics     Open Access   (Followers: 1)
Pure Mathematics and Applications     Open Access  
Pythagoras     Open Access  
Quaestiones Mathematicae     Hybrid Journal  
Qualitative Theory of Dynamical Systems     Hybrid Journal  
Quantum Studies : Mathematics and Foundations     Hybrid Journal   (Followers: 2)
Quarterly Journal of Mathematics     Hybrid Journal  
Rare Metals     Hybrid Journal   (Followers: 2)
Recreational Mathematics Magazine     Open Access  
REDIMAT : Journal of Research in Mathematics Education     Open Access   (Followers: 6)
REMAT : Revista Eletrônica da Matemática     Open Access  
Rendiconti del Circolo Matematico di Palermo     Hybrid Journal  
Reportes Científicos de la FaCEN     Open Access  
Research in Mathematics Education     Hybrid Journal   (Followers: 13)
Research in Nondestructive Evaluation     Hybrid Journal   (Followers: 7)
Research in Number Theory     Hybrid Journal   (Followers: 1)
Research in the Mathematical Sciences     Open Access  
Research Journal of Pure Algebra     Open Access   (Followers: 1)
Researches in Mathematics     Open Access  

  First | 1 2 3 4     

Similar Journals
Journal Cover
Research in Number Theory
Journal Prestige (SJR): 0.754
Number of Followers: 1  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 2522-0160 - ISSN (Online) 2363-9555
Published by SpringerOpen Homepage  [228 journals]
  • Ternary Egyptian fractions with prime denominator

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      Abstract: Abstract For a prime number p, let \(A_3(p)= \{ m \in \mathbb {N}: \exists m_1,m_2,m_3 \in \mathbb {N}, \frac{m}{p}=\frac{1}{m_1}+\frac{1}{m_2}+\frac{1}{m_3} \} \) . In 2019 Luca and Pappalardi proved that \(x (\log x)^3 \ll \sum _{p \le x} A_{3}(p) \ll x (\log x)^5\) . We improve the upper bound, showing \(\sum _{p \le x} A_{3}(p) \ll x (\log x)^3 (\log \log x)^2\) .
      PubDate: 2022-06-26
       
  • Factorizations of bivariate Taylor series via power products

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      Abstract: Abstract Let \(f(x,y)=1+\sum \limits _{\begin{array}{c} p=1\\ m+n=p \end{array}}^{\infty }a_{m,n}x^my^n\) be a formal power series. We convert f(x, y) into the formal product \(\prod \limits _{\begin{array}{c} p=1\\ m+n=p \end{array}}^{\infty }(1+g_{m,n}x^m y^n)\) , namely the power product expansion in two independent variables. By developing new machinery involving the majorizing infinite product, we provide estimates on the domain of absolute convergence of the infinite product via the Taylor series coefficients of f(x, y). This machinery introduces a myriad of “mixed expansions”, uncovers various algebraic connections between the \((a_{m,n})\) and the \((g_{m,n})\) , and leads to the identification of the domain of absolute convergence of the power product as the Cartesian product of polydiscs associated with a quadratic equation. This makes it possible to use the truncated power product expansions \(\prod \limits _{\begin{array}{c} p=1\\ m+n=p \end{array}}^{P}(1+g_{m,n}x^my^n)\) as approximations to the analytic function f(x, y). We derive an asymptotic formula for the \(g_{m,n}\) , with m fixed, associated with the majorizing infinite product. We also discuss various combinatorial interpretations provided by these power product expansions and derive an additional theorem which shows that with \(g_{m,n}\ge 0\) , the polydisc of absolute convergence for the power product is identical to that of its Taylor series.
      PubDate: 2022-06-23
       
  • Packing polynomials on irrational sectors

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      Abstract: Abstract Fueter and Polya proved that the only quadratic polynomials giving a bijection between N and N \(^{2}\) are the two Cantor polynomials. It is conjectured that there is no bijection from N \(^2\) onto N given by a polynomial of degree at least 3. A similar problem arises when the domain of the map is replaced by the set of integral points in some sector in R \(^2\) . Rational sectors were considered by Nathanson and Stanton. Here, we study and solve the case of general irrational sectors. In fact, our method enables us also to recover the results on rational sectors and also answer a question posed by Nathanson.
      PubDate: 2022-06-19
       
  • Normality of the Thue–Morse function for finite fields along
           polynomial values

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      Abstract: Abstract Let \(\varvec{F}_q\) be the finite field of q elements, where \(q=p^r\) is a power of the prime p, and \(\left( \beta _1, \beta _2, \dots , \beta _r \right) \) be an ordered basis of \(\varvec{F}_q\) over \(\varvec{F}_p\) . For $$\begin{aligned} \xi =\sum _{i=1}^rx_i\beta _i, \quad x_i\in \varvec{F}_p, \end{aligned}$$ we define the Thue–Morse or sum-of-digits function \(T(\xi )\) on \(\varvec{F}_q\) by $$\begin{aligned} T(\xi )=\sum _{i=1}^{r}x_i. \end{aligned}$$ For a given pattern length s with \(1\le s\le q\) , a vector \(\varvec{\alpha }=(\alpha _1,\ldots ,\alpha _s)\in \varvec{F}_q^s\) with different coordinates \(\alpha _{j_1}\not = \alpha _{j_2}\) , \(1\le j_1<j_2\le s\) , a polynomial \(f(X)\in \varvec{F}_q[X]\) of degree d and a vector \(\mathbf{c} =(c_1,\ldots ,c_s)\in \varvec{F}_p^s\) we put $$\begin{aligned} \mathcal{T}(\mathbf{c} ,\varvec{\alpha },f)=\{\xi \in \varvec{F}_q : T(f(\xi +\alpha _i))=c_i,~i=1,\ldots ,s\}. \end{aligned}$$ In this paper we will see that under some natural conditions, the size of  \(\mathcal{T}(\mathbf{c} ,\varvec{\alpha },f)\) is asymptotically the same for all  \(\mathbf{c} \) and \(\varvec{\alpha }\) in both cases, \(p\rightarrow \infty \) and \(r\rightarrow \infty \) , respectively. More precisely, we have $$\begin{aligned} \left \mathcal{T}(\mathbf{c} , \varvec{\alpha }, f) - p^{r-s} \right \le (d-1)q^{1/2} \end{aligned}$$ under certain conditions on d, q and s. For monomials of large degree we improve this bound as well as we find conditions on d, q and s for which this bound is not true. In particular, if \(1\le d<p\) we have the dichotomy that the bound is valid if \(s\le d\) and for \(s\ge d+1\) there are vectors \(\mathbf{c} \) and  \(\varvec{\alpha }\) with
      PubDate: 2022-06-12
       
  • On radiuses of convergence of q-metallic numbers and related q-rational
           numbers

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      Abstract: Abstract The q-rational numbers and the q-irrational numbers were introduced by Morier-Genoud and Ovsienko. In this paper, we focus on q-real quadratic irrational numbers, especially q-metallic numbers and q-rational sequences which converge to q-metallic numbers, and consider the radiuses of convergence of them when we assume that q is a complex number. We construct two sequences given by recurrence formula as a generalization of the q-deformation of the Fibonacci and Pell numbers which are introduced by Morier-Genoud and Ovsienko. For these two sequences, we prove a conjecture of Leclere, Morier-Genoud, Ovsienko and Veselov concerning the expected lower bound of the radiuses of convergence. In addition, we obtain a relationship between the radius of convergence of these two sequences in two special cases.
      PubDate: 2022-06-09
       
  • An analogue of Weil’s converse theorem for harmonic Maass forms of
           polynomial growth

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      Abstract: Abstract We construct a family of harmonic Maass forms of polynomial growth of any level corresponding to any cusp whose shadows are Eisenstein series of integral weight. We further consider Dirichlet series attached to a harmonic Maass form of polynomial growth, study its analytic properties, and prove an analogue of Weil’s converse theorem.
      PubDate: 2022-05-25
       
  • A conjectural asymptotic formula for multiplicative chaos in number theory

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      Abstract: Abstract We investigate a special sequence of random variables A(N) defined by an exponential power series with independent standard complex Gaussians \((X(k))_{k \ge 1}\) . Introduced by Hughes, Keating, and O’Connell in the study of random matrix theory, this sequence relates to Gaussian multiplicative chaos (in particular “holomorphic multiplicative chaos” per Najnudel, Paquette, and Simm) and random multiplicative functions. Soundararajan and Zaman recently determined the order of \(\mathbb {E}[ A(N) ]\) . By constructing an algorithm to calculate A(N) in \(O(N^2 \log N)\) steps, we produce computational evidence that their result can likely be strengthened to an asymptotic result with a numerical estimate for the asymptotic constant. We also obtain similar conclusions when A(N) is defined using standard real Gaussians or uniform \(\pm 1\) random variables. However, our evidence suggests that the asymptotic constants do not possess a natural product structure.
      PubDate: 2022-05-23
       
  • Constructing all genus 2 curves with supersingular Jacobian

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      Abstract: Abstract L. Moret-Bailly constructed families \({\mathfrak {C}}\rightarrow {\mathbb {P}}^1\) of genus 2 curves with supersingular Jacobian. In this paper we first classify the reducible fibers of a Moret-Bailly family using linear algebra over a quaternion algebra. The main result is an algorithm that exploits properties of two reducible fibers to compute a hyperelliptic model for any irreducible fiber of a Moret-Bailly family.
      PubDate: 2022-05-18
       
  • Combinatorial Burnside groups

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      Abstract: Abstract We study the structure of combinatorial Burnside groups, which receive equivariant birational invariants of actions of finite groups on algebraic varieties.
      PubDate: 2022-05-18
       
  • Linear relations among Galois conjugates over $${\mathbb {F}}_q(t)$$ F q (
           t )

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      Abstract: Abstract We classify the coefficients \((a_1, \ldots , a_n) \in {\mathbb {F}}_q[t]^n\) that appear in a linear relation \(\sum _{i=1}^n a_i \gamma _i =0\) among Galois conjugates \(\gamma _i \in \overline{{\mathbb {F}}_q(t)}\) . We call such an n-tuple a Smyth tuple. Our main theorem gives an affirmative answer to a function field analogue of a 1986 conjecture of Smyth (J Numb Theory 23, 243–254, 1986) over \({\mathbb {Q}}\) . Smyth showed that certain local conditions on the \(a_i\) are necessary and conjectured that they are sufficient. Our main result is that the analogous conditions are necessary and sufficient over \({\mathbb {F}}_q(t)\) , which we show using a combinatorial characterization of Smyth tuples from Smyth (J Numb Theory 23, 243–254, 1986). We also formulate a generalization of Smyth’s Conjecture in an arbitrary number field that is not a straightforward generalization of the conjecture over \({\mathbb {Q}}\) due to a subtlety occurring at the archimedean places.
      PubDate: 2022-05-18
       
  • A criterion of algebraic independence of values of modular functions and
           

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      Abstract: Abstract The aim of this paper is to give a criterion of algebraic independence for the values at the same point of two modular functions under certain conditions. As an application, we show that any two infinite products in $$\begin{aligned} \prod _{n=1}^{\infty }\left( 1+\frac{1}{F_n} \right) ,\quad \prod _{n=3}^{\infty }\left( 1-\frac{1}{F_n} \right) ,\quad \prod _{n=1}^{\infty }\left( 1+\frac{1}{L_n} \right) ,\quad \prod _{n=2}^{\infty }\left( 1-\frac{1}{L_n} \right) \end{aligned}$$ are algebraically independent over \(\mathbb {Q}\) , where \(\{F_n\}\) and \( \{L_n\} \) are the Fibonacci and Lucas sequences, respectively. The proof of our main theorem is based on the properties of the field of all modular functions for the principal congruence subgroup, together with a deep result of Yu. V. Nesterenko on algebraic independence of the values of the Eisenstein series.
      PubDate: 2022-05-10
       
  • Special zeta Mahler functions

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      Abstract: Abstract We study the zeta Mahler function (ZMF, also zeta Mahler measure), which is closely related to the Mahler measure. Here we discuss a family of ZMFs attached to the Laurent polynomials \(k + (x_1 + x_1^{-1}) \cdots \left( x_r + x_r^{-1}\right) \) , where k is real. We give explicit formulae, present examples and establish properties for these ZMFs, such as an RH-type phenomenon. Further, we explore connections with the Mahler measure.
      PubDate: 2022-04-24
       
  • Totally real bi-quadratic fields with large Pólya groups

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      Abstract: Abstract For an algebraic number field K with ring of integers \(\mathcal {O}_{K}\) , an important subgroup of the ideal class group \(Cl_{K}\) is the Pólya group, denoted by Po(K), which measures the failure of the \(\mathcal {O}_{K}\) -module \(Int(\mathcal {O}_{K})\) of integer-valued polynomials on \(\mathcal {O}_{K}\) from admitting a regular basis. In this paper, we prove that for any integer \(n \ge 2\) , there are infinitely many totally real bi-quadratic fields K with \(Po(K) \simeq ({\mathbb {Z}}/2{\mathbb {Z}})^{n}\) . In fact, we explicitly construct such an infinite family of number fields. This also provides an infinite family of bi-quadratic fields with ideal class groups of 2-ranks at least n.
      PubDate: 2022-04-24
       
  • Splitting of primes in number fields generated by points on some modular
           curves

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      Abstract: Abstract We study the splitting of primes in number fields generated by points on modular curves. Momose (Nagoya Math J 96:139–165, 1984) was the first to notice that quadratic points on \(X_1(N)\) generate quadratic fields over which certain primes split in a particular way and his results were later expanded upon by Krumm (Quadratic Points on Modular Curves. PhD thesis, University of Georgia, 2013). We prove results about the splitting behaviour of primes in quadratic fields generated by points on the modular curves \(X_0(N)\) which are hyperelliptic (except for \(N=37\) ) and in cubic fields generated by points on \(X_1(2,14)\) .
      PubDate: 2022-04-21
       
  • Explicit minimal embedded resolutions of divisors on models of the
           projective line

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      Abstract: Abstract Let K be a discretely valued field with ring of integers \(\mathcal {O}_K\) with perfect residue field. Let K(x) be the rational function field in one variable. Let \({\mathbb {P}}^1_{\mathcal {O}_K}\) be the standard smooth model of \({\mathbb {P}}^1_K\) with coordinate x. Let \(f(x) \in \mathcal {O}_K[x]\) be a squarefree polynomial with corresponding divisor of zeroes \({{\,\mathrm{div}\,}}_0(f)\) on \({\mathbb {P}}^1_{\mathcal {O}_K}\) . We give an explicit description of the minimal embedded resolution \(\mathcal {Y}\) of the pair \(({\mathbb {P}}^1_{\mathcal {O}_K}, {{\,\mathrm{div}\,}}_0(f))\) by using Mac Lane’s theory to write down the discrete valuations on K(x) corresponding to the irreducible components of the special fiber of \(\mathcal {Y}\) .
      PubDate: 2022-04-13
       
  • Bounds on shifted convolution sums for Hecke eigenforms

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      Abstract: Abstract Shifted convolution sums play a prominent rôle in analytic number theory. Here these sums are considered in the context of holomorphic Hecke eigenforms. We investigate pointwise bounds, mean-square bounds consistent with the optimal conjectural bound, and find asymptotics on average for their variance.
      PubDate: 2022-04-08
       
  • Two-variable polynomials with dynamical Mahler measure zero

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      Abstract: Abstract We discuss several aspects of the dynamical Mahler measure for multivariate polynomials. We prove a weak dynamical version of the Boyd–Lawton formula, and we characterize the polynomials with integer coefficients having dynamical Mahler measure zero both for the case of one variable (Kronecker’s lemma) and for the case of two variables, under the assumption that the dynamical version of Lehmer’s question is true.
      PubDate: 2022-03-31
       
  • Bailey pairs and indefinite quadratic forms, II. False indefinite theta
           functions

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      Abstract: Abstract We construct families of Bailey pairs \((\alpha _n,\beta _n)\) where the exponent of q in \(\alpha _n\) is an indefinite quadratic form, but where the usual \((-1)^j\) is replaced by a sign function. This leads to identities involving “false” indefinite binary theta series. These closely resemble q-identities for mock theta functions or Maass waveforms, but the sign function prevents them from having the usual modular properties.
      PubDate: 2022-03-23
       
  • On the Mordell–Weil lattice of $$y^2 = x^3 + b x + t^{3^n + 1}$$ y 2 = x
           3 + b x + t 3 n + 1 in characteristic 3

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      Abstract: Abstract We study the elliptic curves given by \(y^2 = x^3 + b x +t^{3^n+1}\) over global function fields of characteristic 3 ; in particular we perform an explicit computation of the L-function by relating it to the zeta function of a certain superelliptic curve \(u^3 + b u = v^{3^n + 1}\) . In this way, using the Néron–Tate height on the Mordell–Weil group, we obtain lattices in dimension \(2 \cdot 3^n\) for every \(n \ge 1\) , which improve on the currently best known sphere packing densities in dimensions 162 (case \(n=4\) ) and 486 (case \(n=5\) ). For \(n=3\) , the construction has the same packing density as the best currently known sphere packing in dimension 54, and for \(n=1\) it has the same density as the lattice \(E_6\) in dimension 6.
      PubDate: 2022-03-17
       
  • Correction to: A transcendental Brauer–Manin obstruction to weak
           approximation on a Calabi–Yau threefold

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      Abstract: A Correction to this paper has been published: https://doi.org/10.1007/s40993-021-00307-4
      PubDate: 2022-03-07
       
 
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