2011 Fiscal Year Final Research Report
A study of Bernoulli numbers and the distribution of irregular primes
| Project/Area Number |
21540026
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
AGOH Takashi 東京理科大学, 理工学部・数学科, 教授 (60112893)
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| Co-Investigator(Renkei-kenkyūsha) |
KOBAYASHI Takao 東京理科大学, 理工学部・数学科, 教授 (90178319)
TANAKA Ryuichi 東京理科大学, 理工学部・数学科, 教授 (10112898)
HACHIMORI Yoshitaka 東京理科大学, 理工学部・数学科, 准教授 (50433743)
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| Project Period (FY) |
2009 – 2011
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| Keywords | ベルヌイ数 / 代数体の類数 / イデアル類群 / 正則・非正則素数 / 素数分布 |
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| Research Abstract |
We studied special properties of Bernoulli, Genocchi and Stirling numbers of both kinds and discovered new recurrences and higher-order convolution identities. Concerning generalized Frobenuis-Euler numbers and polynomials, we constructed the corresponding L type function after proving basic relations and Kummer type congruences. On the other hand, we discussed new criteria for irregularity of primes and also observed many interesting properties of irregular pairs from numerical experiment.
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