Study on a new divisor problem arisen from the derivatives of the Riemann zeta function
| Project/Area Number |
23740009
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Kyoto Sangyo University |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | リーマンゼータ / ゼータの微分 / 約数問題 / ゼータの零点分布 / マース形式 / マース形式(インド・アラハバード) / カタラン定数 / 国際研究者交流 / インド / グラフのゼータ |
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| Research Abstract |
This research is a new development on the classical Dirichlet divisor problem. Let d(n) be the number of divisor of n (it is called the divisor function). In the average of d(n), to study the error term is called the divisor problem. From an aspect of the study of the derivatives of Riemann zeta function, we define a new divisor function D(k)(n). By this research we obtained a formula on the error term in the average of D(k)(n). It is expressed by a certain finite sum of Bessel functions.
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Report
(4 results)
Research Products
(29 results)
