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Similar Journals
 Lithuanian Mathematical JournalJournal Prestige (SJR): 0.558 Citation Impact (citeScore): 1Number of Followers: 0      Hybrid journal (It can contain Open Access articles) ISSN (Print) 1573-8825 - ISSN (Online) 0363-1672 Published by Springer-Verlag  [2658 journals]
• Foreword

PubDate: 2019-03-09
DOI: 10.1007/s10986-019-09431-2

• Professor Eugenijus Manstavičius

PubDate: 2019-03-09
DOI: 10.1007/s10986-019-09430-3

• Professor Antanas Laurinčikas

PubDate: 2019-03-09
DOI: 10.1007/s10986-019-09429-w

• On the Distribution of Polynomial Discriminants: Totally Real Case

Abstract: We study the distribution of the discriminant D(P) of polynomials P from the class Pn(Q) of all integer polynomials of degree n and height at most Q. We evaluate the asymptotic number of polynomials P ∈ Pn(Q) having all real roots and satisfying the inequality D(P) ≤ X as Q→∞and X/Q2n−2→ 0.
PubDate: 2019-03-06
DOI: 10.1007/s10986-019-09434-z

• On mixed joint discrete universality for a class of zeta-functions. II

Abstract: We investigate the mixed joint discrete value distribution and the mixed joint discrete universality for the pair consisting of a rather general form of zeta-function with an Euler product and a periodic Hurwitz zeta-function with transcendental parameter. The common differences of relevant arithmetic progressions are not necessarily the same. Also some generalizations are given. For this purpose, certain arithmetic conditions on the common differences are used.
PubDate: 2019-03-05
DOI: 10.1007/s10986-019-09432-1

• On a certain set of Lerch’s zeta-functions and their derivatives
∗

Abstract: For 0 < α ≤ 1 and 0 < λ ≤ 1, let L(α, λ, s) denote the associated Lerch zeta-function, which is defined as $${\sum}_{n=0}^{\infty }{\mathrm{e}}^{2\pi \mathrm{i}n\uplambda}{\left(n+\alpha \right)}^{-s}$$ for ℜs > 1. We investigate the joint value-distribution for all Lerch zeta-functions {L(αj, λ, s): 0 < λ ≤ 1, j = 1, … , J} and their derivatives when α1,…, αJ satisfy a certain condition. This condition is satisfied if α1,…, αJ are algebraically independent over ℚ. More precisely, we establish a joint denseness result for values of those functions on vertical lines in the strip 1/2 < ℜs ≤ 1. We also establish the functional independence of those functions in the sense of Voronin.
PubDate: 2019-03-05
DOI: 10.1007/s10986-019-09433-0

• A degree problem for the compositum of two number fields*

Abstract: The triplet (a, b, c) of positive integers is said to be compositum-feasible if there exist number fields K and L of degrees a and b, respectively, such that the degree of their compositum KL equals c. We determine all compositum-feasible triplets (a, b, c) satisfying a ≤ b and b ∈ {8, 9}. This extends the classification of compositum-feasible triplets started by Drungilas, Dubickas, and Smyth [5]. Moreover, we obtain several results related to triplets of the form (a, a, c). In particular, we prove that the triplet (n, n, n(n − 2)) is not compositum-feasible, provided that n ≥ 5 is an odd integer.
PubDate: 2019-03-01
DOI: 10.1007/s10986-019-09428-x

• Modeling the beta distribution in short intervals

Abstract: We prove that any beta distribution can be simulated by means of a sequence of distributions defined via multiplicative functions in a short interval.
PubDate: 2019-02-26
DOI: 10.1007/s10986-019-09427-y

• On the simultaneous rational approximations to real and p -adic numbers

Abstract: We consider simultaneous rational approximations to real and p-adic numbers. We prove that for any irrational number α0 and p-adic number α, there are infinitely many irreducible fractions satisfying ∣α0 − m/n ∣  < 1/n2/3 − ∈ and α0 − m/n p < 1/n2/3 − ∈, where ∈ > 0 is an arbitrary number, and ∣ ⋅  ∣ p is the p-adic norm.
PubDate: 2019-02-23
DOI: 10.1007/s10986-019-09426-z

• On M -functions for the value-distributions of L -functions

Abstract: Bohr and Jessen proved the existence of a certain limit value regarded as the probability that values of the Riemann zeta function belong to a given region in the complex plane. They also studied the density of the probability, which has been called the M-function since the studies of Ihara and Matsumoto. In this paper, we construct M-functions for the value-distributions of L-functions in a class containing many kinds of zeta and L-functions. Moreover, we improve the estimate on the rate of the convergence of the limit studied by Bohr and Jessen.
PubDate: 2019-02-23
DOI: 10.1007/s10986-019-09425-0

• Mahler measure of a difference of two conjugates*

Abstract: Suppose that an algebraic number β of degree d = n(n − 1) over ℚ is expressible by the difference of two conjugate algebraic integers α1 ≠ α2 of degree n, namely, β = α1− α2. We prove that then there exists a constant c > 1, which depends on $$\overline{\mid \alpha \mid }$$ = max1≤i≤n ∣αi∣ only, such that M(β)1/d > c.
PubDate: 2019-02-19
DOI: 10.1007/s10986-019-09424-1

• A central limit theorem for coefficients of the modified Borwein method
for the calculation of the Riemann zeta-function

Abstract: The paper extends the study of the modified Borwein method for the calculation of the Riemann zeta-function. We present an alternative perspective on the proof of the central limit theorem for coefficients of the method. The new approach is based on the connection with the limit theorem applied to asymptotic enumeration.
PubDate: 2019-02-18
DOI: 10.1007/s10986-019-09421-4

• Distribution of Arithmetic Functions on Particular Subsets of Integers

Abstract: Let Q1, . . . , Qt ∈ℝ[x] be polynomials with no constant term for which each linear combination m1Q1(x) + · · ·+mtQt (x) with m1, . . . , mt ∈ℤand not all 0 always has an irrational coefficient. Let I1, . . . , It be sets included in the interval [0, 1), each being a union of finitely many subintervals of [0, 1). Furthermore, let $$\mathcal{T}$$ be the set of positive integers n for which {Q1(n)} ∈ I1, . . . , {Qt(n)} ∈ It simultaneously, where {y} stands for the fractional part of y. Let t1, t2, . . . be a uniformly summable sequence of complex numbers and set T(x) =  ∑ n ≤ xtn and $$T\left(x \mathcal{T}\right)=\sum {}_{n\le x,n\in \mathcal{T}}{t}_n$$ . We prove that, as x→∞, $$T(x)/x\sim T\left(x \ \mathcal{T}\right)/\left(\uplambda \left({I}_1\right)\cdots \uplambda \left({I}_t\right)x\right)$$ , where λ(I) is the Lebesgue measure of a set I.
PubDate: 2019-02-18
DOI: 10.1007/s10986-019-09422-3

• Joint universality of Hurwitz zeta-functions and nontrivial zeros of the
Riemann zeta-function

Abstract: We prove that every collection of analytic functions (f1(s), . . . , fr(s)) defined on the right-hand side of the critical strip can be simultaneously approximated by shifts of Hurwitz zeta-functions (ζ(s + iγκh, α1),  … , ζ(s + iγκh, αr)), h > 0, where 0 < γ1 ≤ γ2 ≤ … are the imaginary parts of nontrivial zeros of the Riemann zeta-function ζ(s). We use the weak form of the Montgomery pair correlation conjecture and the linear independence over ℚ of the set {log(m + αj) : m ∈ ℕ0, j = 1,  … , r}.
PubDate: 2019-02-18
DOI: 10.1007/s10986-019-09423-2

• A generalization of the Voronin theorem

Abstract: The classical Voronin universality theorem asserts that a wide class of analytic functions can be approximated by shifts of the Riemann zeta-function ζ(s + iτ), τ ∈ ℝ. In the paper, we generalize this approximation for shifts ζ(s + iφ(τ)), where ðœ‘(τ) has the monotonic positive derivative such that 1/ðœ‘′(τ) = o(τ) and φ(2τ) × maxτ ≪ t ≪ 2τ(1/φ′(t)) ≪ τ as τ →∞.
PubDate: 2019-01-18
DOI: 10.1007/s10986-019-09418-z

• On some explicit evaluations of nonlinear Euler sums

Abstract: In this paper, we extend tools developed in [26] to study harmonic numbers sums. We use these objects to compute Euler-related sums and to explore their connections with classical Euler sums. We establish some new relations between Euler sums and related sums. The relations obtained allow us to find some nice closed-form representations of nonlinear Euler sums through zeta values and linear sums.
PubDate: 2019-01-18
DOI: 10.1007/s10986-019-09420-5

• Solvability of second-order coupled systems on the half-line

Abstract: In this work, we consider a second-order coupled system of differential equations in semiinfinite intervals. The arguments apply the fixed point theory, Green’s functions technique, L1-Carathéodory functions theory, a truncation technique, and Schauder’s fixed point theorem. The technique used consists in application of a Nagumo-type growth condition to nonlinearities and the concept of equiconvergence for recovering the compactness of the associated operators. In the last section, we present an example.
PubDate: 2019-01-18
DOI: 10.1007/s10986-019-09419-y

• Semi-Heavy Tails

Abstract: In this paper, we study properties of functions and sequences with a semi-heavy tail, that is, functions and sequences of the form w(x) = e−βxf(x), β > 0, resp., wn = cnfn, 0 < c < 1, where the function f(x), resp., the sequence (fn), is regularly varying. Among others, we give a representation theorem and study convolution properties. The paper includes several examples and applications in probability theory.
PubDate: 2018-10-01
DOI: 10.1007/s10986-018-9417-0

• Risk aggregation based on the Poisson INAR(1) process with periodic
structure

Abstract: In this paper, we consider a risk model by introducing a temporal dependence between the claim numbers under periodic environment, which generalizes several discrete-time risk models. The model proposed is based on the Poisson INAR(1) process with periodic structure. We study the moment-generating function of the aggregate claims. The distribution of the aggregate claims is discussed when the individual claim size is exponentially distributed.
PubDate: 2018-10-01
DOI: 10.1007/s10986-018-9412-5

• Exponential probabilistic inequalities

Abstract: We extend the mapping properties of martingale transforms, decoupling inequalities, differential subordination, and the Stein inequalities to exponential Orlicz spaces.
PubDate: 2018-10-01
DOI: 10.1007/s10986-018-9410-7

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Heriot-Watt University
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