EULERIANITY OF FOURIER COEFFICIENTS OF AUTOMORPHIC FORMS

Dmitry Gourevitch, Henrik P.A. Gustafsson, Axel Kleinschmidt, Daniel Persson, Siddhartha Sahi

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)481-507
Number of pages27
JournalRepresentation Theory
Volume25
DOIs
StatePublished - 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

Keywords

  • Eisenstein series
  • Euler product
  • Fourier coefficients on reductive groups
  • Fourier-Jacobi coefficients
  • Whittaker support
  • automorphic forms
  • automorphic representation
  • minimal representation
  • next-to-minimal representation
  • nilpotent orbit
  • wave-front set

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