
arXiv: 1505.02263
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].
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
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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