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2019 Weyl bound for $p$-power twist of $\mathrm{GL}(2)$ $L$-functions
Ritabrata Munshi, Saurabh Kumar Singh
Algebra Number Theory 13(6): 1395-1413 (2019). 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 ( 1 2 + i t , f χ ) f , t , ε p r + ε ,

where ε > 0 is any positive real number.

Citation

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Ritabrata Munshi. Saurabh Kumar Singh. "Weyl bound for $p$-power twist of $\mathrm{GL}(2)$ $L$-functions." Algebra Number Theory 13 (6) 1395 - 1413, 2019. https://doi.org/10.2140/ant.2019.13.1395

Information

Received: 9 July 2018; Revised: 12 March 2019; Accepted: 10 April 2019; Published: 2019
First available in Project Euclid: 21 August 2019

zbMATH: 07103978
MathSciNet: MR3994569
Digital Object Identifier: 10.2140/ant.2019.13.1395

Subjects:
Primary: 11F66
Secondary: 11F55 , 11M41

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

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.13 • No. 6 • 2019
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