The universality for linear combinations of Lerch zeta functions and the Tornheim–Hurwitz type of double zeta functions

Abstract

In this paper, we consider the universality for linear combinations of Lerch zeta functions. J. Kaczorowski, A. Laurincikas and J. Steuding treated universal Dirichlet series with the case that the compact sets \({\mathcal{K}_l}\) are disjoint. But we consider the both cases that the compact subset \({\mathcal{K}_l}\) is disjoint and not disjoint. Next, we will show the non-trivial zeros of the Tornheim–Hurwitz type of double zeta functions in the region of absolute convergence. Moreover we show the universality for the Tornheim–Hurwitz type of double zeta function.