Eulerianity of Fourier coefficients of automorphic forms

2020/04/29 by Gourevitch, Dmitry, Gustafsson, Henrik P. A., Kleinschmidt, Axel +2
#11F30 #11F70 #20G45 #22E55 #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2004.14244

Abstract

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.

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