Results 1 to 10 of about 260 (137)

Automorphic forms with degenerate Fourier coefficients

American Journal of Mathematics, 1997
The main theme of this paper is that singular automorphic forms on classical groups are given by theta series liftings. We establish several inequalities relating the automorphic multiplicities of a given representation and that of its abstract theta ...
Jian-Shu Li
exaly   +4 more sources

Fourier coefficients of automorphic forms, character variety orbits, and small representations

Journal of Number Theory, 2012
TextWe 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 G2, we perform an analysis of the ...
Siddhartha Sahi
exaly   +5 more sources

Computation of Fourier coefficients of automorphic forms of type $$G_2$$

Research in Number Theory
In a recent work, we found formulas for the Fourier coefficients of automorphic forms of type $G_2$: holomorphic Siegel modular forms on $\mathrm{Sp}_6$ that are theta lifts from $G_2^c$, and cuspidal quaternionic modular forms on split $G_2$.
Aaron Pollack
exaly   +5 more sources

A reduction principle for Fourier coefficients of automorphic forms [PDF]

Mathematische Zeitschrift, 2022
We consider a special class of unipotent periods for automorphic forms on a finite cover of a reductive adelic group G(AK) , which we refer to as Fourier coefficients associated to the data of a ‘Whittaker pair’.
Gourevitch, Dmitry,, Kleinschmidt, Axel, Sahi, Siddhartha, Kleinschmidt, A., Gustafsson, Henrik, Persson, Daniel, Sahi, S., Gustafsson, Henrik P. A.,, Gourevitch, D., Sahi, Siddhartha,, Kleinschmidt, Axel,, Persson, Daniel,, Gourevitch, Dmitry, Gustafsson, Henrik,   +13 more
core   +7 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.
Gourevitch, Dmitry,, Kleinschmidt, Axel, Sahi, Siddhartha, Gustafsson, H., Kleinschmidt, A., Gustafsson, Henrik, Sahi, S., Persson, Daniel, Gustafsson, Henrik P. A.,, Gourevitch, D., Persson, D., Sahi, Siddhartha,, Kleinschmidt, Axel,, Persson, Daniel,, Gourevitch, Dmitry, Gustafsson, Henrik,   +15 more
core   +4 more sources

The Arithmetic of the Fourier Coefficients of Automorphic Forms [PDF]

, 2023
This thesis studies modular forms from a classical and adelic viewpoint. We use this interplay to obtain results about the arithmetic of the Fourier coefficients of modular forms and their generalisations.
Davis, T
core   +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, Bhakta, Subham, Finder, Renan   +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 R Booker
exaly   +3 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 ...
RICOTTA, Guillaume, KOWALSKI, Emmanuel
core   +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 ...
Baiying Liu, Liu Baiying
exaly   +3 more sources