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A reduction principle for Fourier coefficients of automorphic forms.

Authors :
Gourevitch, Dmitry
Gustafsson, Henrik P. A.
Kleinschmidt, Axel
Persson, Daniel
Sahi, Siddhartha
Source :
Mathematische Zeitschrift; Mar2022, Vol. 300 Issue 3, p2679-2717, 39p
Publication Year :
2022

Abstract

We consider a special class of unipotent periods for automorphic forms on a finite cover of a reductive adelic group G (A K) , which we refer to as Fourier coefficients associated to the data of a 'Whittaker pair'. We describe a quasi-order on Fourier coefficients, and an algorithm that gives an explicit formula for any coefficient in terms of integrals and sums involving higher coefficients. The maximal elements for the quasi-order are 'Levi-distinguished' Fourier coefficients, which correspond to taking the constant term along the unipotent radical of a parabolic subgroup, and then further taking a Fourier coefficient with respect to a K -distinguished nilpotent orbit in the Levi quotient. Thus one can express any Fourier coefficient, including the form itself, in terms of higher Levi-distinguished coefficients. In companion papers we use this result to determine explicit Fourier expansions of minimal and next-to-minimal automorphic forms on split simply-laced reductive groups, and to obtain Euler product decompositions of certain Fourier coefficients. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00255874
Volume :
300
Issue :
3
Database :
Complementary Index
Journal :
Mathematische Zeitschrift
Publication Type :
Academic Journal
Accession number :
155238736
Full Text :
https://doi.org/10.1007/s00209-021-02784-w