Omega theorems for a class of $L$-functions (A note on the Ranking-Selberg zeta-function)

Abstract

In this paper we study the Omega theorems for a class of general $L$-functions satisfying certain conditions and as an important application, we obtain the Omega theorems for the Rankin-Selberg zeta-functions $Z(s_0)$ attached to holomorphic cusp forms of fixed weight for the full modular group when $\frac {1}{2}\le \sigma_0<1$.