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Journal of Functional Analysis
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Fourier coefficients of automorphic forms and integrable discrete series

Authors: Muić, Goran;

Fourier coefficients of automorphic forms and integrable discrete series

Abstract

Let $G$ be the group of $\mathbb R$--points of a semisimple algebraic group $\mathcal G$ defined over $\mathbb Q$. Assume that $G$ is connected and noncompact. We study Fourier coefficients of Poincar\' e series attached to matrix coefficients of integrable discrete series. We use these results to construct explicit automorphic cuspidal realizations, which have appropriate Fourier coefficients $\neq 0$, of integrable discrete series in families of congruence subgroups. In the case of $G=Sp_{2n}(\mathbb R)$, we relate our work to that of Li [15]. For $\mathcal G$ quasi--split over $\mathbb Q$, we relate our work to the result about Poincar\' e series due to Khare, Larsen, and Savin [16].

Country
Croatia
Keywords

cuspidal automorphic form, Mathematics - Number Theory, Cuspidal Automorphic Forms, Poincaré series, Fourier coefficients of automorphic forms, Semisimple Lie groups and their representations, Representation-theoretic methods; automorphic representations over local and global fields, Fourier coefficient, Cuspidal Automorphic Forms, Poincare Series, Fourier coefficients., FOS: Mathematics, Poincare Series, representation semisimple Lie group, Number Theory (math.NT), Representation Theory (math.RT), Fourier coefficients., Mathematics - Representation Theory

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
Green
hybrid