A reduction principle for Fourier coefficients of automorphic forms

نویسندگان

چکیده

Abstract We consider a special class of unipotent periods for automorphic forms on finite cover reductive adelic group $$\mathbf {G}(\mathbb {A}_\mathbb {K})$$ G ( A K ) , 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

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ژورنال

عنوان ژورنال: Mathematische Zeitschrift

سال: 2021

ISSN: ['1432-1823', '0025-5874']

DOI: https://doi.org/10.1007/s00209-021-02784-w