Back to Search Start Over

LARGE VALUES OF L-FUNCTIONS ON THE 1-LINE

Authors :
Anup B. Dixit
Kamalakshya Mahatab
Source :
Bulletin of the Australian Mathematical Society. 103:230-243
Publication Year :
2020
Publisher :
Cambridge University Press (CUP), 2020.

Abstract

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 arbitrarily 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 generalisation of the result of Aistleitner, Munsch and Mahatab [‘Extreme values of the Riemann zeta function on the $1$ -line’, Int. Math. Res. Not. IMRN2019(22) (2019), 6924–6932]. 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.

Details

ISSN :
17551633 and 00049727
Volume :
103
Database :
OpenAIRE
Journal :
Bulletin of the Australian Mathematical Society
Accession number :
edsair.doi...........017a2dd78e47ec25774db17ed2e3ea0e
Full Text :
https://doi.org/10.1017/s0004972720000647