Startseite A shifted convolution sum for \mathrm{GL}(3) × \mathrm{GL}(2)
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A shifted convolution sum for \mathrm{GL}(3) × \mathrm{GL}(2)

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Veröffentlicht/Copyright: 10. Januar 2018

Abstract

In this paper, we estimate the shifted convolution sum

n1λ1(1,n)λ2(n+h)V(nX),

where V is a smooth function with support in [1,2], 1|h|X, and λ1(1,n) and λ2(n) are the n-th Fourier coefficients of SL(3,𝐙) and SL(2,𝐙) Hecke–Maass cusp forms, respectively. We prove an upper bound O(X2122+ε), updating a recent result of Munshi.


Communicated by Freydoon Shahidi


Award Identifier / Grant number: 11601413

Award Identifier / Grant number: 2017JQ1016

Funding statement: The work is supported in part by NSFC (No.11601413) and NSBRP (No. 2017JQ1016) of Shaanxi Province.

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Received: 2017-11-02
Published Online: 2018-01-10
Published in Print: 2018-07-01

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