| Project/Area Number |
15K04778
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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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, 招へい教員 (50109261)
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| Co-Investigator(Renkei-kenkyūsha) |
MINAMIDE Makoto 山口大学, 大学院創成科学研究科, 講師 (80596552)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 短区間平均値定理 / 数論的誤差項 / Tong型の公式 / 3 次元約数問題 / 符号変化 / shifted convolution / リーマンゼータ関数の導関数 / 近似関数等式 / Tong 型の公式 / ３次約数問題 / トング型の公式 / ヴォロノイ公式 / ゼータ関数の微分 / Tong型公式 / 数論的誤差項の符号変化 / shifted convolusion |
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| Outline of Final Research Achievements |
We derived the mean square formula in short intervals for an arithmetical error term by using the Tong-type truncated formula which we had already established for zeta-functions in the extended Selberg class. We applied our theorems to the study of the three-dimensional divisor problems and got the new results for the shifted convolutions and the sign changes of its arithmetical error term. Furthermore,we remade our Tong-type truncated formula in term of the exponent of the mean square of the zeta-function on the critical line.
In 1999, Hall derived the approximate functional equations for the square of the derivative of the Reimann zeta-function and other functions. By generalizing the method of Titchmarsh, we improved the estimates of Hall's error terms.
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