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 general semisimple algebraic group $G$ defined over a number field $k$ such that its Archimedean group $G_{\mathrm{\infty }}$ is not compact. When $G$ is quasi–split over $k$, we obtain a result on existence of generic cuspidal automorphic representations which generalize a result of Vign' eras, Henniart, and Shahidi. We also discuss the existence of cuspidal automorphic forms with non–zero Fourier coefficients for congruence of subgroups of $G_{\mathrm{\infty }}$.