Averages of shifted convolutions of general divisor sums involving Hecke eigenvalues

Dan Wang ()
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Dan Wang: Qilu University of Technology (Shandong Academy of Sciences)

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 2, 443-453

Abstract: Abstract Suppose $$\sum _{n=1}^{\infty }a(n) n^{-s}$$ ∑ n = 1 ∞ 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 $$\sum _{n\leqslant x}a(n)$$ ∑ n ⩽ 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].

Keywords: Shifted convolutions; Hecke eigenvalue; Mean square estimate in short interval; Truncated Tong-type formula; 11F30; 11F37; 11M41; 11N37 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13226-021-00107-7

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