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

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.

References in corpus (4)

• Lattice points in large regions and related arithmetic functions: Recent developments in a very classic topic
• On sums of Fourier coefficients of cusp forms
• On the Tong-type identity and the mean square of the error term for an extended Selberg class
• Mean square of the error term in the asymmetric many dimensional divisor problem

Cited by in corpus (4)

• On the Tong-type identity and the mean square of the error term for an extended Selberg class
• Mean square of the error term in the asymmetric many dimensional divisor problem
• The Average Size of Ramanujan Sums over Cubic Number Fields
• On the sum of ${\Delta }_k(n)$ in the Piltz divisor problem for $k=3$ and $k=4$