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LARGE VALUES OF L-FUNCTIONS ON THE 1-LINE
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society / Volume 103 / Issue 2 / April 2021
- Published online by Cambridge University Press:
- 02 October 2020, pp. 230-243
- Print publication:
- April 2021
-
- Article
- Export citation
-
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. IMRN 2019(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.
