Results 1 to 10 of about 112 (98)
A reduction principle for Fourier coefficients of automorphic forms [PDF]
Mathematische Zeitschrift, 2021 AbstractWe consider a special class of unipotent periods for automorphic forms on a finite cover of a reductive adelic group $$\mathbf {G}(\mathbb {A}_\mathbb {K})$$ G ( A K )
Dmitry Gourevitch +2 more
exaly +4 more sources
Fourier coefficients of GL(N) automorphic forms in arithmetic progressions [PDF]
Geometric and Functional Analysis, 2014 We show that the multiple divisor functions of integers in invertible residue classes modulo a prime number, as well as the Fourier coefficients of GL(N) Maass cusp forms for all N larger than 2, satisfy a central limit theorem in a suitable range, generalizing the case N=2 treated by E. Fouvry, S. Ganguly, E. Kowalski and P. Michel.
Emmanuel Kowalski, Kowalski Emmanuel
exaly +3 more sources
Growth of Fourier coefficients of vector-valued automorphic forms
Journal of Number Theory, 2023 In this article, we establish polynomial-growth bound for the sequence of Fourier coefficients associated to even integer weight vector-valued automorphic forms of Fuchsian groups of the first kind. At the end, their $L$-functions and exponential sums have been discussed.
Bajpai, Jitendra +2 more
exaly +5 more sources
A Test for Identifying Fourier Coefficients of Automorphic Forms and Application to Kloosterman Sums [PDF]
Experimental Mathematics, 2000 We present a numerical test for determining whether a given set of numbers is the set of Fourier coefficients of a Maass form, without knowing its eigenvalue. Our method extends directly to consideration of holomorphic newforms. The test is applied to show that the Kloosterman sums ±S(l, 1; p)/√p are not the coefficients of a Maass form with small ...
Andrew Booker
exaly +3 more sources
Arthur Parameters and Fourier coefficients for Automorphic Forms on Symplectic Groups [PDF]
Annales De L'Institut Fourier, 2016 We study the structures of Fourier coefficients of automorphic forms on symplectic groups based on their local and global structures related to Arthur parameters. This is a first step towards the general conjecture on the relation between the structure of Fourier coefficients and Arthur parameters for automorphic forms occurring in the discrete ...
Dihua Jiang, Baiying Liu, Liu Baiying
exaly +3 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.
Shimura Goro, Goro Shimura
exaly +2 more sources
Fourier coefficients of automorphic forms, character variety orbits, and small representations
Journal of Number Theory, 2012 We consider the Fourier expansions of automorphic forms on general Lie groups, with a particular emphasis on exceptional groups. After describing some principles underlying known results on GL(n), Sp(4), and G_2, we perform an analysis of the expansions on split real forms of E_6 and E_7 where simplifications take place for automorphic realizations of ...
Siddhartha Sahi
exaly +4 more sources
Eulerianity of Fourier coefficients of automorphic forms [PDF]
Representation Theory, 2021 We study the question of Eulerianity (factorizability) for Fourier coefficients of automorphic forms, and we prove a general transfer theorem that allows one to deduce the Eulerianity of certain coefficients from that of another coefficient. We also establish a ‘hidden’ invariance property of Fourier coefficients.
Gourevitch, D. +4 more
openaire +3 more sources
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