Large values of L-functions on 1-line

2019/01/06 by Dixit, Anup B., Mahatab, Kamalakshya · 1 citation
#11M41 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1901.01625

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 exists arbitrary large t such that F(1+it)≥ e^γ_F (log₂ t + log₃ t)^m + O(1), 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.

Cited by

• Extreme values of derivatives of the Dedekind zeta function of a cyclotomic field

Related

• Extreme values of the Riemann zeta function on the 1-line
• Large values of L-functions from the Selberg class
• On derivatives of zeta and L-functions near the 1-line
• Joint Extreme values of L-functions
• Explicit bounds for the Riemann zeta-function on the 1-line