2013 Fiscal Year Final Research Report
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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| 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 |
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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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Research Products
(16 results)
