On the mean square of an arithmetical error term of the Selberg class in short intervals-Reference-Cited by-同舟云学术

On the mean square of an arithmetical error term of the Selberg class in short intervals

Published:2016-07-26 Issue:06 Volume:12 Page:1675-1701
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Cao Xiaodong¹,Tanigawa Yoshio²,Zhai Wenguang³

Affiliation:

1. Department of Mathematics and Physics, Beijing Institute of Petro-Chemical Technology, Beijing 102617, P. R. China

2. Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan

3. Department of Mathematics, China University of Mining and Technology, Beijing 100083, P. R. China

Abstract

Let [Formula: see text] be a Dirichlet series in the Selberg class of degree [Formula: see text] and let [Formula: see text] be the arithmetical error term of [Formula: see text]. We derive two kinds of the mean square estimates of [Formula: see text] in short intervals of Jutila’s type. Our method is based on the truncated Tong-type formula of [Formula: see text]. We also give several applications of these estimates in the arithmetical problems.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042116501037

Reference21 articles.

1. Averages of shifted convolutions ofd3(n)

2. On the Bethe-Sommerfeld conjecture for the polyharmonic operator

3. The distribution and moments of the error term in the Dirichlet divisor problem

4. Sign Changes of E(T), Δ(x), and P(x)

5. Some Asymptotic Formulae in the Theory of Numbers

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Averages of shifted convolutions of general divisor sums involving Hecke eigenvalues;Indian Journal of Pure and Applied Mathematics;2021-06-15

2. Tong-type identity and the mean square of the error term for an extended Selberg class;Science China Mathematics;2016-07-22