Dirichlet series obtained from the error term in the Dirichlet divisor problem

In this paper we consider the Dirichlet series obtained from the error term in the Dirichlet divisor problem. We shall prove their analytic continuations and determine the locations of poles. We shall also discuss the relation between our results and the conjecture of Lau and Tsang on the mean squar...

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Bibliographic Details
Published inMonatshefte für Mathematik Vol. 160; no. 4; pp. 385 - 402
Main Authors Furuya, J., Tanigawa, Y., Zhai, W.
Format Journal Article
LanguageEnglish
Published Vienna Springer Vienna 01.07.2010
Subjects
Mathematics
Mathematics and Statistics
The Dirichlet divisor problem
11L07
11M41
Mean square estimate
Analytic continuation
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Summary:In this paper we consider the Dirichlet series obtained from the error term in the Dirichlet divisor problem. We shall prove their analytic continuations and determine the locations of poles. We shall also discuss the relation between our results and the conjecture of Lau and Tsang on the mean square estimate of the error term.
ISSN:0026-9255
1436-5081
DOI:10.1007/s00605-010-0195-y