Large values of $L$-functions on $1$-line

Abstract

In this paper, we study lower bounds of a general family of L-functions on the 1-line. More precisely, we show that for any F (s) in this family, there exist arbitrary large t such that, where m is the order of the pole of F (s) at s = 1. This is a generalization of the same result of Aistleitner, Munsch and the second author for the Riemann zeta-function. As a consequence, we get lower bounds for large values of Dedekind zeta-functions and Rankin-Selberg L-functions of the type L(s, f ×f ) on the 1-line.2010 Mathematics Subject Classification. 11M41.