Abstract
We obtain a discrete universality theorem on the approximation of analytic functions by shifts of L-functions of normalized Hecke-eigen cusp forms with respect to congruence subgroups. Such a result is already proved in the authors’ previous paper [A. Lauriňcikas, K. Matsumoto, and J. Steuding, Discrete universality of L-functions for new forms, Math. Notes, 78(4):551–558, 2005] under a certain arithmetical condition, which we remove in this paper. Also, we present discrete analogues of results of [A. Lauriňcikas, K. Matsumoto, and J. Steuding, Universality of some functions related to zeta-functions of certain cusp forms, Osaka J. Math., 50(4):1021–1037, 2013].
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