| Project/Area Number |
26887035
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Josai University (2015)
Tokyo Denki University (2014) |
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Principal Investigator |
Sono Keiju 城西大学, 理学部, 助教 (10735989)
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| Project Period (FY) |
2014-08-29 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2014: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
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| Keywords | ゼータ関数 / L-関数 / 保型形式 / 素数分布 / リーマン予想 / 解析的整数論 / 保型L-関数 |
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| Outline of Final Research Achievements |
During these two years I have studied the following two objects. The first is the evaluation of the rate of simple zeros of Dirichlet L-functions, and the second is the evaluation of the moments of quadratic twists of automorphic L-functions at the central point. I proved that assuming the generalized Riemann hypothesis, at least 93％ of zeros of primitive Dirichlet L-functions are simple. In the second theme, assuming several hypotheses, I proved that these moments are bounded by the expected order. I have talked about these results at several symposiums in Japan. I have submitted two papers on these results to some international journals and fortunately the papers were accepted.
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