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

Authors

Saurabh Kumar Singh, Indian Statistical Institute, Kolkata

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

Recommended Citation

Singh, Saurabh Kumar, "On double shifted convolution sum of SL(2,Z) Hecke eigenforms" (2018). Journal Articles. 1221.
https://digitalcommons.isical.ac.in/journal-articles/1221