Fourier Coefficients of Automorphic Forms and Integrable Discrete Series

2015/05/09 by Muić, Goran
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1505.02263

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 ≠ 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].

Related

• On Existence of Generic Cusp Forms on Semisimple Algebraic Groups
• Smooth cuspidal automorphic forms and integrable discrete series
• Fourier coefficients for automorphic forms on quasisplit classical groups
• On a family of Siegel Poincaré series
• Fourier coefficients of minimal and next-to-minimal automorphic\n representations of simply-laced groups