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Mathematics > Number Theory

arXiv:1501.04269 (math)
[Submitted on 18 Jan 2015]

Title:On the Tong-type identity and the mean square of the error term for an extended Selberg class

Authors:Xiaodong Cao, Yoshio Tanigawa, Wenguang Zhai
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Abstract:In 1956, Tong established an asymptotic formula for the mean square of the error term in the summatory function of the Piltz divisor function $d_3(n).$ The aim of this paper is to generalize Tong's method to a class of Dirichlet series that satisfy a functional equation. As an application, we can establish the asymptotic formulas for the mean square of the error terms for a class of functions in the well-known Selberg class. The Tong-type identity and formula established in this paper can be viewed as an analogue of the well-known Voronoï's formula.
Subjects: Number Theory (math.NT)
Cite as: arXiv:1501.04269 [math.NT]
  (or arXiv:1501.04269v1 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1501.04269
Related DOI: https://doi.org/10.1007/s11425-015-0706-2

Submission history

From: Xiaodong Cao [view email]
[v1] Sun, 18 Jan 2015 06:45:57 UTC (50 KB)
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