Vol. 13, No. 6, 2019

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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 Γ0(N) with N square-free. Let p be a prime and let χ be a primitive character of modulus p3r. We shall prove the Weyl-type subconvex bound

L(1 2 + it,f χ) f,t,εpr+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