A reduction principle for Fourier coefficients of automorphic forms

• DOI: 10.1007/s00209-021-02784-w
• Publication Date: 2021-10-15T16:40:41Z
• Authors: Dmitry Gourevitch; Henrik P. A. Gust...; Axel Kleinschmidt; Daniel Persson; Siddhartha Sahi
• Keywords: Unipotent

Abstract We consider a special class of unipotent periods for automorphic forms on finite cover reductive adelic group $$\mathbf {G}(\mathbb {A}_\mathbb {K})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>G</mml:mi> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>A</mml:mi> <mml:mi>K</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , which we refer to as Fourier coefficients associated the data ‘Whittaker pair’. describe quasi-order coefficients, and an algorithm that gives explicit formula any coefficient in terms integrals sums involving higher coefficients. The maximal elements are ‘Levi-distinguished’ correspond taking constant term along radical parabolic subgroup, then further with respect $${\mathbb K}$$ -distinguished nilpotent orbit Levi quotient. Thus one can express coefficient, including form itself, Levi-distinguished In companion papers use this result determine expansions minimal next-to-minimal split simply-laced groups, obtain Euler product decompositions certain