EULERIANITY OF FOURIER COEFFICIENTS OF AUTOMORPHIC FORMS
Journal article, 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. We apply these results to minimal and next-to-minimal automorphic representations, and deduce Eulerianity for a large class of Fourier and Fourier-Jacobi coefficients. In particular, we prove Eulerianity for parabolic Fourier coefficients with characters of maximal rank for a class of Eisenstein series in minimal and next-to-minimal representations of groups of ADE-type that are of interest in string theory.

Euler product

nilpotent orbit

Eisenstein series

minimal representation

next-to-minimal representation

Whittaker support

automorphic forms

wave-front set

automorphic representation

Fourier coefficients on reductive groups

Fourier-Jacobi coefficients

Author

Dmitry Gourevitch

Weizmann Institute of Science

Henrik Gustafsson

Institute for Advanced Studies

Rutgers University

Chalmers, Mathematical Sciences, Algebra and geometry

Axel Kleinschmidt

Max Planck Society

Université libre de Bruxelles (ULB)

Daniel Persson

Chalmers, Mathematical Sciences, Algebra and geometry

Siddhartha Sahi

Rutgers University

Representation Theory

1088-4165 (ISSN)

Vol. 25 481-507

Små automorfa representationer

Swedish Research Council (VR) (2018-04760), 2019-01-01 -- 2022-12-31.

Subject Categories

Geometry

Discrete Mathematics

Mathematical Analysis

DOI

10.1090/ert/565

More information

Latest update

7/5/2021 2