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arXiv · 1501.04269

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

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.

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Xiaodong Cao, Yoshio Tanigawa, Wenguang Zhai. 2015-01-18. On the Tong-type identity and the mean square of the error term for an extended Selberg class. https://doi.org/10.1007/s11425-015-0706-2

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