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Averages of shifted convolutions of general divisor sums involving Hecke eigenvalues

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Abstract

Suppose \(\sum _{n=1}^{\infty }a(n) n^{-s}\) be a Dirichlet series in the Selberg class of degree d and let E(x) be the arithmetical error term of \(\sum _{n\leqslant x}a(n)\). By the truncated Tong-type formula of E(x), we can get two kinds of the mean square estimates of E(x) in short intervals of Jutila’s type. Using the estimates, we are able to improve some previous results established by Lü and Wang [9].

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Acknowledgements

The author is very grateful to the reviewers for many valuable suggestions and comments.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan, 250353, Shandong, China

    Dan Wang

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  1. Dan Wang
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Correspondence to Dan Wang.

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Communicated by Eknath Ghate, Ph.D.

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Wang, D. Averages of shifted convolutions of general divisor sums involving Hecke eigenvalues. Indian J Pure Appl Math 53, 443–453 (2022). https://doi.org/10.1007/s13226-021-00107-7

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  • DOI: https://doi.org/10.1007/s13226-021-00107-7

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