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.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Euler product

Fourier coefficients on reductive groups

Fourier-Jacobi

coefficients

automorphic forms

automorphic representation

minimal

representation

next-to-minimal representation

Whittaker support

nilpotent orbit

wave-front set

Eisenstein series

small representations

minimal representations

eisenstein series

exceptional group

constructions

Mathematics

Publikations- och innehållstyp

ref (ämneskategori)

art (ämneskategori)