Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract We state and prove a formula for the adjoint of the nullwert map from spaces of Jacobi cusp forms of lattice index to spaces of modular forms. Furthermore, we prove a nonvanishing result for the image of the adjoint of the nullwert map. PubDate: 2024-07-25
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract In this paper we study the theta lifting of a weight 2 Bianchi modular form \({\mathcal {F}}\) of level \(\Gamma _0({\mathfrak {n}})\) with \({\mathfrak {n}}\) square-free to a weight 2 holomorphic Siegel modular form. Motivated by Prasanna’s work for the Shintani lifting, we define the local Schwartz function at finite places using a quadratic Hecke character \(\chi \) of square-free conductor \({\mathfrak {f}}\) coprime to level \({\mathfrak {n}}\) . Then, at certain 2 by 2 g matrices \(\beta \) related to \({\mathfrak {f}}\) , we can express the Fourier coefficient of this theta lifting as a multiple of \(L({\mathcal {F}},\chi ,1)\) by a non-zero constant. If the twisted L-value is known to be non-vanishing, we can deduce the non-vanishing of our theta lifting. PubDate: 2024-07-19
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract To any V in the Grassmannian \(\textrm{Gr}_k({\mathbb R}^n)\) of k-dimensional vector subspaces in \({\mathbb {R}}^n\) one can associate the diagonal entries of the ( \(n\times n\) ) matrix corresponding to the orthogonal projection of \({\mathbb {R}}^n\) to V. One obtains a map \(\textrm{Gr}_k({\mathbb {R}}^n)\rightarrow {\mathbb {R}}^n\) (the Schur–Horn map). The main result of this paper is a criterion for pre-images of vectors in \({\mathbb {R}}^n\) to be connected. This will allow us to deduce connectivity criteria for a certain class of subspaces of the real Stiefel manifold which arise naturally in frame theory. We extend in this way results of Cahill et al. (SIAM J Appl Algebra Geom 1:38–72, 2017). PubDate: 2024-05-06 DOI: 10.1007/s12188-024-00277-1
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract Let X be a K3 surface, let C be a smooth curve of genus g on X, and let A be a line bundle of degree d on C. Then a line bundle M on X with \(M\otimes {\mathcal {O}}_C=A\) is called a lift of A. In this paper, we prove that if the dimension of the linear system A is \(r\ge 2\) , \(g>2d-3+(r-1)^2\) , \(d\ge 2r+4\) , and A computes the Clifford index of C, then there exists a base point free lift M of A such that the general member of M is a smooth curve of genus r. In particular, if A is a base point free net which defines a double covering \(\pi :C\longrightarrow C_0\) of a smooth curve \(C_0\subset {\mathbb {P}}^2\) of degree \(k\ge 4\) branched at distinct 6k points on \(C_0\) , then, by using the aforementioned result, we can also show that there exists a 2:1 morphism \({\tilde{\pi }}:X\longrightarrow {\mathbb {P}}^2\) such that \({\tilde{\pi }} _C=\pi \) . PubDate: 2024-04-16 DOI: 10.1007/s12188-024-00275-3
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract Let K be a number field and G a finitely generated torsion-free subgroup of \(K^\times \) . Given a prime \(\mathfrak {p}\) of K we denote by \({{\,\textrm{ind}\,}}_\mathfrak {p}(G)\) the index of the subgroup \((G\bmod \mathfrak {p})\) of the multiplicative group of the residue field at \(\mathfrak {p}\) . Under the Generalized Riemann Hypothesis we determine the natural density of primes of K for which this index is in a prescribed set S and has prescribed Frobenius in a finite Galois extension F of K. We study in detail the natural density in case S is an arithmetic progression, in particular its positivity. PubDate: 2024-04-09 DOI: 10.1007/s12188-024-00276-2
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract In this paper, when \(1<p<2\) , we establish the \(C^{1,\alpha }_{\,\textrm{loc}\,}\) -regularity of weak solutions to the degenerate subelliptic p-Laplacian equation $$\begin{aligned} \triangle _{{{\mathcal {H}}},p}u(x)=\sum \limits _{i=1}^6X^*_i( {\nabla _{{{\mathcal {H}}}}u} ^{p-2}X_iu)=0 \end{aligned}$$ on SU(3) endowed with the horizontal vector fields \(X_1,\dots ,X_6\) . The result can be extended to a class of compact connected semi-simple Lie group. PubDate: 2024-03-18 DOI: 10.1007/s12188-024-00274-4
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract In this paper, we consider biconservative and biharmonic isometric immersions into the 4-dimensional Lorentzian space form \({\mathbb {L}}^4(\delta )\) with constant sectional curvature \(\delta \) . We obtain some local classifications of biconservative CMC surfaces in \({\mathbb {L}}^4(\delta )\) . Further, we get complete classification of biharmonic CMC surfaces in the de Sitter 4-space. We also proved that there is no biharmonic CMC surface in the anti-de Sitter 4-space. Further, we get the classification of biconservative, quasi-minimal surfaces in Minkowski-4 space. PubDate: 2024-01-29 DOI: 10.1007/s12188-023-00273-x
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract We study base-point-freeness for big and nef line bundles on hyperkähler manifolds of generalized Kummer type: For \(n\in \{2,3,4\}\) , we show that, generically in all but a finite number of irreducible components of the moduli space of polarized \(\textrm{Kum}^n\) -type varieties, the polarization is base-point-free. We also prove generic base-point-freeness in the moduli space in all dimensions if the polarization has divisibility one. PubDate: 2023-11-16 DOI: 10.1007/s12188-023-00271-z
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract In this paper, we see that the hypersurfaces \(\mathcal {L}_{\pm }\) in Ando (Abh Math Semin Univ Hambg 92:105–123, 2022, Proposition 1) are neutral but not flat. Nonetheless, we find parallel almost complex structures \(\mathcal {I}_{\pm }\) suitable for Ando (Abh Math Semin Univ Hambg 92:105–123, 2022, Theorem 1) and parallel almost paracomplex structures \(\mathcal {J}_{\pm }\) suitable for Ando (Abh Math Semin Univ Hambg 92:105–123, 2022, Theorem 2). PubDate: 2023-11-13 DOI: 10.1007/s12188-023-00272-y
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract In his 2008 thesis [16] , Tateno claimed a counterexample to the Bonato–Tardif conjecture regarding the number of equimorphy classes of trees. In this paper we revisit Tateno’s unpublished ideas to provide a rigorous exposition, constructing locally finite trees having an arbitrary finite number of equimorphy classes; an adaptation provides partial orders with a similar conclusion. At the same time these examples also disprove conjectures by Thomassé and Tyomkyn. PubDate: 2023-11-01 DOI: 10.1007/s12188-023-00270-0
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract We study lines on smooth cubic surfaces over the field of p-adic numbers, from a theoretical and computational point of view. Segre showed that the possible counts of such lines are 0, 1, 2, 3, 5, 7, 9, 15 or 27. We show that each of these counts is achieved. Probabilistic aspects are investigated by sampling both p-adic and real cubic surfaces from different distributions and estimating the probability of each count.We link this to recent results on probabilistic enumerative geometry. Some experimental results on the Galois groups attached to p-adic cubic surfaces are also discussed. PubDate: 2023-09-16 DOI: 10.1007/s12188-023-00269-7
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract We call a smooth irreducible projective curve a Castelnuovo curve if it admits a birational map into the projective r-space such that the image curve has degree at least 2r+1 and the maximum possible geometric genus (which one can calculate by a classical formula due to Castelnuovo). It is well known that a Castelnuovo curve must lie on a Hirzebruch surface (rational ruled surface). Conversely, making use of a result of W. Castryck and F. Cools concerning the scrollar invariants of curves on Hirzebruch surfaces we show that curves on Hirzebruch surfaces are Castelnuovo curves unless their genus becomes too small w.r.t. their gonality. We analyze the situation more closely, and we calculate the number of moduli of curves of fixed genus g and fixed gonality k lying on Hirzebruch surfaces, in terms of g and k. PubDate: 2023-06-08 DOI: 10.1007/s12188-023-00267-9
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract In 2020 S. M. Gonek, S. W. Graham and Y. Lee formulated the Lindelöf hypothesis for prime numbers and proved that it is equivalent to the Riemann Hypothesis. In this note we show that their result holds in the Selberg class of L-functions. PubDate: 2023-05-17 DOI: 10.1007/s12188-023-00268-8
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract We find and discuss an unexpected (to us) order n cyclic group of automorphisms of the Lie algebra \(I{\mathfrak u}_n{:}{=}{\mathfrak u}_n < imes {\mathfrak u}_n^*\) , where \({\mathfrak u}_n\) is the Lie algebra of upper triangular \(n\times n\) matrices. Our results also extend to \(\mathfrak {gl}_{n+}^\epsilon \) , a “solvable approximation” of \(\mathfrak {gl}_n\) , as defined within. PubDate: 2023-03-16 DOI: 10.1007/s12188-023-00266-w
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract We show that every compact complex analytic space endowed with a fine logarithmic structure and every morphism between such spaces admit a semi-universal deformation. These results generalize the analogous results in complex analytic geometry first independently proved by A. Douady and H. Grauert in the ’70. We follow Douady’s two steps process approach consisting of an infinite-dimensional construction of the deformation space followed by a finite-dimensional reduction. PubDate: 2023-02-24 DOI: 10.1007/s12188-023-00264-y
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract In this paper, we firstly generalize the Brunn–Minkowski type inequality for Ekeland–Hofer–Zehnder symplectic capacity of bounded convex domains established by Artstein-Avidan–Ostrover in 2008 to extended symplectic capacities of bounded convex domains constructed by authors based on a class of Hamiltonian non-periodic boundary value problems recently. Then we introduce a class of non-periodic billiards in convex domains, and for them we prove some corresponding results to those for periodic billiards in convex domains obtained by Artstein-Avidan–Ostrover in 2012. PubDate: 2023-02-23 DOI: 10.1007/s12188-023-00263-z
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract We study the nontrivial elements in the Brauer group of a bielliptic surface and show that they can be realized as Azumaya algebras with a simple structure at the generic point of the surface. We go on to study some properties of the noncommutative Picard scheme associated to such an Azumaya algebra. PubDate: 2023-02-14 DOI: 10.1007/s12188-023-00265-x
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract We study the existence and uniqueness of renormalized solutions for initial boundary value problems of the type $$\begin{aligned} \left( {\mathcal {P}}_{b}^{1}\right) \quad \left\{ \begin{aligned} u_{t}-\text {div}(a(t,x,\nabla u))=H(u)\mu \text { in }Q:=(0,T)\times \Omega ,\\ u(0,x)=u_{0}(x)\text { in }\Omega ,\ u(t,x)=0\text { on }(0,T)\times \partial \Omega , \end{aligned}\right. \end{aligned}$$ where \(u_{0}\in L^{1}(\Omega )\) , \(\mu \in {\mathcal {M}}_{b}(Q)\) is a general Radon measure on Q and \(H\in C_{b}^{0}({\mathbb {R}})\) is a continuous positive bounded function on \({\mathbb {R}}\) . The difficulties in the study of such problems concern the possibly very singular right-hand side that forces the choice of a suitable formulation that ensures both existence and uniqueness of solution. Using similar techniques, we will prove existence/nonexistence results of the auxiliary problem $$\begin{aligned} \left( {\mathcal {P}}_{b}^{2}\right) \quad \left\{ \begin{aligned}&u_{t}-\text {div}(a(t,x,\nabla u))+g(x,u) \nabla u ^{2}=\mu \text { in }Q:=(0,T)\times \Omega ,\\&u(0,x)=u_{0}(x)\text { in }\Omega ,\ u(t,x)=0\text { on }(0,T)\times \partial \Omega , \end{aligned}\right. \end{aligned}$$ under the assumption that g satisfies a sign condition and the nonlinear term depends on both x, u and its gradient. Thus, our results improve and complete the previous known existence results for problems \(\left( {\mathcal {P}}_{b}^{1,2}\right) \) . PubDate: 2022-12-13 DOI: 10.1007/s12188-022-00262-6
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract Carmesin has extended Robertson and Seymour’s tree-of-tangles theorem to the infinite tangles of locally finite infinite graphs. We extend it further to the infinite tangles of all infinite graphs. Our result has a number of applications for the topology of infinite graphs, such as their end spaces and their compactifications. PubDate: 2022-11-29 DOI: 10.1007/s12188-022-00259-1
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract In this article we study the relation between flat solvmanifolds and \(G_2\) -geometry. First, we give a classification of 7-dimensional flat splittable solvmanifolds using the classification of finite subgroups of \(\mathsf{GL}(n,\mathbb {Z})\) for \(n=5\) and \(n=6\) . Then, we look for closed, coclosed and divergence-free \(G_2\) -structures compatible with the flat metric on them. In particular, we provide explicit examples of compact flat manifolds with a torsion-free \(G_2\) -structure whose finite holonomy is cyclic and contained in \(G_2\) , and examples of compact flat manifolds admitting a divergence-free \(G_2\) -structure. PubDate: 2022-11-11 DOI: 10.1007/s12188-022-00261-7
Hybrid journal (It can contain Open Access articles)
[2468 journals]
