2011 Fiscal Year Final Research Report
Analytic properties of the error term arising from the arithmetical problems
| Project/Area Number |
21540012
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Nagoya University |
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Principal Investigator |
TANIGAWA Yoshio 名古屋大学, 多元数理科学研究科, 准教授 (50109261)
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| Co-Investigator(Renkei-kenkyūsha) |
KANEMITSU Shigeru 近畿大学, 産業理工学部, 教授 (60117091)
KIUCHI Isao 山口大学, 大学院・理工学研究科, 教授 (30271076)
FURUYA Jun 沖縄工業高等専門学校, 総合科学科, 講師 (10413890)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 約数問題 / 円問題 / 数論的誤差項 / チャウラ-ワールムの和 / ベルヌーイ多項式 / リーマンゼータ関数 / 多重ゼータ関数 / 平均値定理 |
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| Research Abstract |
First we studied the analytic properties of the Dirichlet series obtained by the arithmetical error term, especially by the error termΔ(x) arising from the Dirichlet divisor problems. We also derived the explicit formula of the integral involvingΔ(x). Secondly we treated the sum of Chowla and Walum. We succeeded to improve its upper bound by using the theory of exponent pairs. We also got an improvement of its mean square formula. As a generalization of our study, we considered closely the difference of the discrete and continuous mean square formulas of the error term obtained from the general divisor problems by using the generalized sum of Chowla and Walum.
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