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EXTREME VALUES OF THE RANKIN–SELBERG 
$\boldsymbol {L}$-FUNCTIONS
Published online by Cambridge University Press: 21 March 2022
Abstract
In this paper, we study the extreme values of the Rankin–Selberg L-functions associated with holomorphic cusp forms in the vertical direction. Assuming the generalised Riemann hypothesis (GRH), we prove that
$$ \begin{align*} \underset{T^{\delta}\leq t\leq T}{\max}\bigg\lvert L\bigg(\frac12+it,f\times f\bigg)\bigg\rvert \geq\exp\bigg(C\sqrt{\frac{\log T\log\log\log T}{\log\log T}}\bigg) \end{align*} $$
with
$C\leq \mathscr {X}\sqrt {1-\delta }$
, where
$\mathscr {X}:=({2}/{\pi })\int _{0}^{\pi /3}\sin ^2\xi \,d\xi $
and
$0\leq \delta <1$
.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 106 , Issue 3 , December 2022 , pp. 408 - 418
- Copyright
- © The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.
Footnotes
This work is supported by the Science and Technology Development Fund, Macau SAR (File No. 0066/2020/A2).
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