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Journal Article

Eulerianity of Fourier coefficients of automorphic forms

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Kleinschmidt,  Axel
Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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2004.14244.pdf
(Preprint), 757KB

S1088-4165-2021-00565-0.pdf
(Publisher version), 392KB

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Citation

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.


Cite as: http://hdl.handle.net/21.11116/0000-0006-67DD-E
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.