Eulerianity of Fourier coefficients of automorphic forms
Copyright policy )Eulerianity of Fourier coefficients of automorphic forms
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.
- Max Planck Society Germany
- Weizmann Institute of Science Israel
- Institute for Advanced Study United States
- Chalmers University of Technology Sweden
- Rutgers, The State University of New Jersey United States
High Energy Physics - Theory, Applications of linear algebraic groups to the sciences, FOS: Physical sciences, automorphic representation, automorphic forms, Euler product, Whittaker support, Fourier coefficients of automorphic forms, minimal representation, nilpotent orbit, FOS: Mathematics, Number Theory (math.NT), Representation Theory (math.RT), 11F30, 11F70, 22E55, 20G45, Mathematics - Number Theory, Fourier-Jacobi coefficients, Representations of Lie and linear algebraic groups over global fields and adèle rings, Fourier coefficients on reductive groups, Representation-theoretic methods; automorphic representations over local and global fields, Eisenstein series, High Energy Physics - Theory (hep-th), next-to-minimal representation, wave-front set, Mathematics - Representation Theory
High Energy Physics - Theory, Applications of linear algebraic groups to the sciences, FOS: Physical sciences, automorphic representation, automorphic forms, Euler product, Whittaker support, Fourier coefficients of automorphic forms, minimal representation, nilpotent orbit, FOS: Mathematics, Number Theory (math.NT), Representation Theory (math.RT), 11F30, 11F70, 22E55, 20G45, Mathematics - Number Theory, Fourier-Jacobi coefficients, Representations of Lie and linear algebraic groups over global fields and adèle rings, Fourier coefficients on reductive groups, Representation-theoretic methods; automorphic representations over local and global fields, Eisenstein series, High Energy Physics - Theory (hep-th), next-to-minimal representation, wave-front set, Mathematics - Representation Theory
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