Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2023; 38(2): 319-330

Online first article April 19, 2023      Printed April 30, 2023

https://doi.org/10.4134/CKMS.c210366

Copyright © The Korean Mathematical Society.

Estimates for certain shifted convolution sums involving Hecke eigenvalues

Guodong Hua

Shandong University

Abstract

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In this paper, we obtain certain estimates for averages of shifted convolution sums involving Hecke eigenvalues of classical holomorphic cusp forms. This generalizes some results of L\"{u} and Wang in this direction.

Keywords: Shifted convolution sums, holomorphic cusp form, automorphic $L$-function

MSC numbers: Primary 11F30, 11F66, 11E20

Supported by: This work was financially supported in part by The National Key Research and Development Program of China (Grant No. 2021YFA1000700) and Natural Science Basic Research Program of Shaanxi (Program Nos. 2023-JC-QN-0024, 2023-JC-YB-077).

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