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  Eulerianity of Fourier coefficients of automorphic forms

Gourevitch, D., Gustafsson, H. P. A., Kleinschmidt, A., Persson, D., & Sahi, S. (2021). Eulerianity of Fourier coefficients of automorphic forms. Representation theory, 25, 481-507. doi:10.1090/ert/565.

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 Creators:
Gourevitch, Dmitry, Author
Gustafsson, Henrik P. A., Author
Kleinschmidt, Axel1, Author           
Persson, Daniel, Author
Sahi, Siddhartha, Author
Affiliations:
1Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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Free keywords: Mathematics, Number Theory, math.NT,High Energy Physics - Theory, hep-th,Mathematics, Representation Theory, math.RT,
 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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 Dates: 2020-04-292020-05-102021
 Publication Status: Issued
 Pages: 27 pages. v2: Clarified connection to Fourier-Jacobi coefficients and references added
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Title: Representation theory
Source Genre: Journal
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Pages: - Volume / Issue: 25 Sequence Number: - Start / End Page: 481 - 507 Identifier: -