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In the paper, joint discrete universality theorems on the simultaneous approximation of a collection of analytic functions by a collection of discrete shifts of zeta-functions attached to normalized Hecke-eigen cusp forms are obtained. These shifts are defined by means of nonlinear differentiable functions that satisfy certain growth conditions, and their combination on positive integers is uniformly distributed modulo 1.

On joint approximation of analytic functions by nonlinear shifts of zeta-functions of certain cusp forms