engleski

On existence of generic cusp forms on semisimple algebraic groups

In this paper we discuss the existence of certain classes of cuspidal automorphic representations having non-zero Fourier coefficients for a general semisimple algebraic group $ G$ defined over a number field $ k$ such that its Archimedean group $ G_\infty $ is not compact. When $ G$ is quasi-split over $ k$, we obtain a result on existence of generic cuspidal automorphic representations which generalize results of Vignéras, Henniart, and Shahidi. We also discuss: (i) the existence of cuspidal automorphic forms with non-zero Fourier coefficients for congruence of subgroups of $ G_\infty $, and (ii) applications related to the work of Bushnell and Henniart on generalized Whittaker models.

Cuspidal automorphic forms ; Poincar'e series ; Fourier coefficients

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