Joint Universality of the Zeta-Functions of Cusp Forms

Abstract

Let F be the normalized Hecke-eigen cusp form for the full modular group and ζ(s,F) be the corresponding zeta-function. In the paper, the joint universality theorem on the approximation of a collection of analytic functions by shifts (ζ(s+ih1τ,F),…,ζ(s+ihrτ,F)) is proved. Here, h1,…,hr are algebraic numbers linearly independent over the field of rational numbers.