Selberg Zeta Functions Have Second Moment At $\sigma =1$

Abstract

In this paper, we demonstrate the existence of the second moment of the Selberg zeta function for a cofinite Fuchsian group at $\sigma =1$. Note that by employing the recent approach of Broucke and Hilberdink in proving the second moment theorem, we can circumvent the separation condition introduced by Landau for general Dirichlet series.

12 pages, 0 figures