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

Anup B. Dixit; Kamalakshya Mahatab

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arXiv · 1901.01625

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

Anup B. Dixit·Kamalakshya Mahatab

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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 $F(1+it)\geq e^{\gamma_F} (\log_2 t + \log_3 t)^m + O(1)$, 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 $L(s,f\times f)$ on the $1$-line.

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BibTeX RIS

Anup B. Dixit, Kamalakshya Mahatab. 2019-01-06. Large values of $L$-functions on $1$-line. https://arxiv.org/abs/1901.01625

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