Hybrid universality theorem for L-functions without Euler product

Abstract

In this paper, we show an analog of hybrid universality theorem (see Ł. Pańkowski, Hybrid joint universality theorem for Dirichlet L-functions, Acta Arith. 141(1) (2010), pp. 59–72) for L-functions without Euler product like Lerch zeta-functions and periodic Hurwitz zeta-functions. More precisely, we prove that any analytic functions can be approximated by some L-functions shifted by iτ and, simultaneously, finitely many real numbers can be approximated by α1τ, …,α n τ, where α1, …,α n are real numbers linearly independent over ℚ.