Eulerianity of Fourier coefficients of automorphic forms

Gourevitch, Dmitry; Gustafsson, Henrik; Kleinschmidt, Axel; Persson, Daniel; Sahi, Siddhartha

doi:10.1090/ert/565

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Eulerianity of Fourier coefficients of automorphic forms

Authors: Dmitry Gourevitch, Henrik P. A. Gustafsson, Axel Kleinschmidt, Daniel Persson and Siddhartha Sahi
Journal: Represent. Theory 25 (2021), 481-507
MSC (2020): Primary 11F30, 11F70, 22E55, 20G45
DOI: https://doi.org/10.1090/ert/565
Published electronically: June 7, 2021
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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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