Weyl bound for p-power twist of GL(2) L-functions

Munshi, Ritabrata; Singh, Saurabh Kumar

doi:10.2140/ant.2019.13.1395

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Weyl bound for $p$-power twist of $\mathrm{GL}(2)$ $L$-functions

Ritabrata Munshi and Saurabh Kumar Singh

Vol. 13 (2019), No. 6, 1395–1413

DOI: 10.2140/ant.2019.13.1395

Abstract

Let $f$ be a cuspidal eigenform (holomorphic or Maass) for the congruence group $Γ_{0} (N)$ with $N$ square-free. Let $p$ be a prime and let $χ$ be a primitive character of modulus $p^{3 r}$ . We shall prove the Weyl-type subconvex bound

L (\frac{1}{2} + i t, f \otimes χ) ≪_{f, t, ε} p^{r + ε},

where $ε > 0$ is any positive real number.

Keywords

Maass forms, Hecke eigenforms, Voronoi summation formula, Poisson summation formula

Mathematical Subject Classification 2010

Primary: 11F66

Secondary: 11F55, 11M41

Milestones

Received: 9 July 2018

Revised: 12 March 2019

Accepted: 10 April 2019

Published: 18 August 2019

Authors

Ritabrata Munshi
Stat-Math Unit Indian Statistical Institute AN Kolmogorov Bhavan Kolkata India

Saurabh Kumar Singh
Stat-Math Unit Indian Statistical Institute AN Kolmogorov Bhavan Kolkata India

Vol. 13, No. 6, 2019