A reduction principle for Fourier coefficients of automorphic forms
Journal article, 2021

We consider a special class of unipotent periods for automorphic forms on a finite cover of a reductive adelic group G(AK) , 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.

Fourier expansion on covers of reductive groups

Whittaker support

Nilpotent orbit

Wave-front set

Automorphic function

Automorphic representation


Dmitry Gourevitch

Weizmann Institute of Science

Henrik Gustafsson

University of Gothenburg

Rutgers University

Chalmers, Mathematical Sciences, Algebra and geometry

Institute for Advanced Studies

Axel Kleinschmidt

International Solvay Institute for Physics and Chemistry

Max Planck Society

Daniel Persson

Chalmers, Mathematical Sciences, Algebra and geometry

Siddhartha Sahi

Rutgers University

Mathematische Zeitschrift

0025-5874 (ISSN) 1432-8232 (eISSN)

Vol. In Press

Subject Categories

Algebra and Logic


Mathematical Analysis



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