Results 11 to 20 of about 260 (137)
Fourier coefficients of automorphic forms and integrable discrete series
Journal of Functional Analysis, 2016 Let $G$ be the group of $\mathbb R$--points of a semisimple algebraic group $\mathcal G$ defined over $\mathbb Q$. Assume that $G$ is connected and noncompact. We study Fourier coefficients of Poincar\' e series attached to matrix coefficients of integrable discrete series.
Göran Muic
exaly +5 more sources
Euler products and Fourier coefficients of automorphic forms on symplectic groups
Inventiones Mathematicae, 1994 The standard \(L\)-function attached to a Siegel modular form of degree \(n\) (or more generally an automorphic form on the adelic symplectic group of rank \(n\)) has been the subject of a great deal of work; a survey of the history of this can be found in the introduction of this article.
Goro Shimura, Shimura Goro
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On special unipotent orbits and Fourier coefficients for automorphic forms on symplectic groups
Journal of Number Theory, 2015 48 pages. Accepted by Journal of Number Theory (Mar. 2014)
Baiying Liu
exaly +4 more sources
Sobolev norms of automorphic functionals and Fourier coefficients of cusp forms
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 1998 . We propose a new approach to the study of eigenfunctions of the LaplaceBeltrami operator on a Riemann surface of curvature -1. It is based on Frobenius reciprocity from the theory of automorphic functions.
Bernstein, Joseph, Reznikov, André
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Fourier expansion of light‐cone Eisenstein series
Journal of the London Mathematical Society, Volume 108, Issue 6, Page 2175-2247, December 2023., 2023 Abstract In this work, we give an explicit formula for the Fourier coefficients of Eisenstein series corresponding to certain arithmetic lattices acting on hyperbolic n+1$n+1$‐space. As a consequence, we obtain results on location of all poles of these Eisenstein series as well as their supremum norms.
Dubi Kelmer, Shucheng Yu
wiley +1 more source
Aspects of the screw function corresponding to the Riemann zeta‐function
Journal of the London Mathematical Society, Volume 108, Issue 4, Page 1448-1487, October 2023., 2023 Abstract We introduce a screw function corresponding to the Riemann zeta‐function and study its properties from various aspects. Typical results are several equivalent conditions for the Riemann hypothesis in terms of the screw function. One of them can be considered an analog of so‐called Weil's positivity or Li's criterion.
Masatoshi Suzuki
wiley +1 more source
A Burgess-like subconvex bound for twisted L-functions [PDF]
, 2007 Let g be a cuspidal newform (holomorphic or Maass) of arbitrary level and nebentypus, X a primitive character of conductor q, and s a point on the critical line Rs = 1/2.
Michel, Philippe +6 more
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Monodromy of four‐dimensional irreducible compatible systems of Q$\mathbb {Q}$
Bulletin of the London Mathematical Society, Volume 55, Issue 4, Page 1773-1790, August 2023., 2023 Abstract Let F$F$ be a totally real field and n⩽4$n\leqslant 4$ a natural number. We study the monodromy groups of any n$n$‐dimensional strictly compatible system {ρλ}λ$\lbrace \rho _\lambda \rbrace _\lambda$ of λ$\lambda$‐adic representations of F$F$ with distinct Hodge–Tate numbers such that ρλ0$\rho _{\lambda _0}$ is irreducible for some λ0$\lambda ...
Chun Yin Hui
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Mathematika, Volume 69, Issue 1, Page 250-285, January 2023., 2023 Abstract We introduce a class of multiplicative functions in which each function satisfies some statistic conditions, and then prove that the above functions are not correlated with finite degree polynomial nilsequences. Besides, we give two applications of this result. One is that the twisting of coefficients of automorphic L‐function on GLm(m⩾2)$GL_m
Xiaoguang He, Mengdi Wang
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Fourier coefficients attached to small automorphic representations of SLn(A) [PDF]
, 2018 We show that Fourier coefficients of automorphic forms attached to minimal or next-to-minimal automorphic representations of SLn(A) are completely determined by certain highly degenerate Whittaker coefficients. We give an explicit formula for the Fourier
Kleinschmidt, Axel +21 more
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