On analytic behaviour of zeta-function and its applications to the arithmetical error term
| Project/Area Number |
24540015
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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, 准教授 (50109261)
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| Co-Investigator(Renkei-kenkyūsha) |
FURUYA Jun 浜松医科大学, 医学部総合人間科学講座, 教授 (10413890)
MINAMIDE Makoto 山口大学, 大学院理工学研究科, 講師 (80596552)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 数論的誤差項 / ディリクレ約数問題 / 多次元非対称約数問題 / Tong タイプの公式 / ２乗平均 / 微分約数問題 / 離散和と連続和 / Tongタイプの公式 / 短区間平均値定理 / 約数問題 / 非対称多次元約数問題 / ヴォロノイ公式 / チャウラ-ワールムの公式 / exponent pair / ベルヌーイ多項式 / ２乗平均値定理 / セルバーグクラス |
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| Outline of Final Research Achievements |
We derived the truncated Tong-type formula for the arithmetical error term arising from the sum of the coeffcients of a zeta function in an extended Selberg class. We applied our formula to the 3-dimensional asymetric divisor problems and got an asymptotic formula of the mean square of the error term. This gives a partial answer of the conjecture of Ivic (1987). We gave a new formula for the difference between the discrete and continuous sum of the arithmetical error term. By this formula, we gave new estimates for the difference of higher power moments case and of the Rankin-Selberg case. We considered the product of k and l-th derivatives of the Riemann zeta function. We derived a certain certain representation of the arithmetical error term arising form this product and gave an upper bound using the theory of exponent pairs. This gives an improvement of Minamide's previous result.
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Report
(4 results)
Research Products
(16 results)
