Results 11 to 20 of about 1,094 (45)
On a convolution series attached to a Siegel Hecke cusp form of degree 2
Ramanujan Journal, 2013 We prove that the "naive" convolution Dirichlet series D_2(s) attached to a degree 2 Siegel Hecke cusp form F, has a pole at s=1. As an application, we write down the asymptotic formula for the partial sums of the squares of the eigenvalues of $F$ with ...
Das, Soumya +2 more
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Airy sheaves for reductive groups
Proceedings of the London Mathematical Society, Volume 126, Issue 1, Page 390-428, January 2023., 2023 Abstract We construct a class of ℓ$\ell$‐adic local systems on A1$\mathbb {A}^1$ that generalizes the Airy sheaves defined by N. Katz to reductive groups. These sheaves are finite field analogues of generalizations of the classical Airy equation y′′(z)=zy(z)$y^{\prime \prime }(z)=zy(z)$. We employ the geometric Langlands correspondence to construct the
Konstantin Jakob +2 more
wiley +1 more source
sl(2)$\mathfrak {sl}(2)$‐Type singular fibres of the symplectic and odd orthogonal Hitchin system
Journal of Topology, Volume 15, Issue 1, Page 1-38, March 2022., 2022 Abstract We define and parametrize so‐called sl(2)$\mathfrak {sl}(2)$‐type fibres of the Sp(2n,C)$\mathsf {Sp}(2n,\mathbb {C})$‐ and SO(2n+1,C)$\mathsf {SO}(2n+1,\mathbb {C})$‐Hitchin system. These are (singular) Hitchin fibres, such that spectral curve establishes a 2‐sheeted covering of a second Riemann surface Y$Y$.
Johannes Horn
wiley +1 more source
Heegner points in Coleman families
Proceedings of the London Mathematical Society, Volume 122, Issue 1, Page 124-152, January 2021., 2021 Abstract We construct two‐parameter analytic families of Galois cohomology classes interpolating the étale Abel–Jacobi images of generalised Heegner cycles, with both the modular form and Grössencharacter varying in p‐adic families.
Dimitar Jetchev +2 more
wiley +1 more source
Non-vanishing of $L$-functions associated to cusp forms of half-integral weight
, 2013 In this article, we prove non-vanishing results for $L$-functions associated to holomorphic cusp forms of half-integral weight on average (over an orthogonal basis of Hecke eigenforms). This extends a result of W.
G. Shimura +7 more
core +1 more source
, 2016 It is proved, that a foliation on a modular curve given by the vertical trajectories of holomorphic differential corresponding to the Hecke eigenform is either the Strebel foliation or the pseudo-Anosov foliation.Comment: to appear Bulletin of the ...
F Diamond +5 more
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Rigidity of p-adic cohomology classes of congruence subgroups of GL(n, Z)
, 2006 We extend the work of Ash and Stevens [Ash-Stevens 97] on p-adic analytic families of p-ordinary arithmetic cohomology classes for GL(N,Q) by introducing and investigating the concept of p-adic rigidity of arithmetic Hecke eigenclasses.
Ash, Avner +2 more
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Anticyclotomic p-adic L-function of central critical Rankin-Selberg L-value
, 2010 Let M be an imaginary quadratic field, f a Hecke eigenform on GL2(Q) and \pi the unitary base-change to M of the automorphic representation associated to f. Take a unitary arithmetic Hecke character \chi of M inducing the inverse of the central character
Brakočević, Miljan
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On the Hecke Eigenvalues of Maass Forms [PDF]
, 2014 Let $\phi$ denote a primitive Hecke-Maass cusp form for $\Gamma_o(N)$ with the Laplacian eigenvalue $\lambda_\phi=1/4+t_{\phi}^2$. In this work we show that there exists a prime $p$ such that $p\nmid N$, $|\alpha_{p}|=|\beta_{p}| = 1$, and $p\ll(N(1+|t_{\
Luo, Wenzhi, Zhou, Fan
core
The weight reduction of mod $p$ Siegel modular forms for $GSp_4$
, 2019 In this paper we investigate the (classical) weights of mod $p$ Siegel modular forms of degree 2 toward studying Serre's conjecture for $GSp_4$. We first construct various theta operators on the space of such forms a la Katz and define the theta cycles ...
Yamauchi, Takuya
core