On joint approximation of analytic functions by nonlinear shifts of zeta-functions of certain cusp forms - Laurinčikas, Antanas; Šiaučiūnas, Darius; Vaiginytė, Adelė (Nonlinear Analysis: Modelling and Control, 2020)
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.
Keywords: Hecke-eigen cusp form; joint universality; uniform distribution modulo 1; zeta-function of cusp form