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
10884165 (eISSN)
Vol. 25 481-507Små 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