"On double shifted convolution sum of SL(2,Z) Hecke eigenforms" by Saurabh Kumar Singh
 

On double shifted convolution sum of SL(2,Z) Hecke eigenforms

Article Type

Research Article

Publication Title

Journal of Number Theory

Abstract

Let λi(n), i=1,2,3, denote the normalized Fourier coefficients of a holomorphic eigenform or Maass cusp form. In this paper we shall consider the sum: S:=[Formula presented]∑H≤h≤2HV([Formula presented])×∑N≤n≤2Nλ1(n)λ2(n+h)λ3(n+2h)W([Formula presented]), where V and W are smooth bump functions, supported on [1,2]. We shall prove a nontrivial upper bound, under the assumption that H≥N1/2+ϵ.

First Page

258

Last Page

272

DOI

10.1016/j.jnt.2018.03.008

Publication Date

10-1-2018

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