2012 Fiscal Year Final Research Report
The origin of analytic properties of zeta functions on the domain where they are divergent
| Project/Area Number |
22740019
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Nagasaki University |
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Principal Investigator |
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| Project Period (FY) |
2010 – 2012
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| Keywords | 数論 / ディリクレ級数 / ゼータ関数 / 解析接続 / 係数和の評価 |
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| Research Abstract |
Let F(s) be a Dirichlet series associated with a sequence a(n). We studied the origin of analytic properties of F(s) from the point of view of an error term coming from sum of a(n).We prove that if m-tuple integrals of the error term are bounded by functions having mild orders, then F(s) can be continued analytically over the whole plane and satisfy a certain additional assumption. The converse assertion is also proved. We also study a relation between values of the m-tuple integrals of the error term and special values of a certain Dirichlet series.
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