2006 Fiscal Year Final Research Report Summary
Research on determinantal formulae and Bernoulli-Hurwitz numbers in the theory of Abelian functions
| Project/Area Number |
16540002
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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 | Iwate University |
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Principal Investigator |
ONISHI Yoshihiro Iwate University, Faculty of Humanities and Social Sciences, Assistant Professor, 人文社会科学部, 助教授 (60250643)
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| Co-Investigator(Kenkyū-buntansha) |
ODAI Yoshitaka Iwate University, Faculty of Humanities and Social Sciences, Assistant Professor, 人文社会科学部, 助教授 (10204215)
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| Project Period (FY) |
2004 – 2006
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| Keywords | Abelian function / Algebraic function / Algebraic curve / hyperelliptic curve / division polynomial / Frobenius-Stickelberger |
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| Research Abstract |
Thanks to the Grant-in-Aid for Scientific Research (C), academic years 2000-2002, with theme "Research on product formula for special values of Abelian functions", the head investigator (Y.O) made two progresses :
(1)Nicely generalized Bernoulli-Hurwitz numbers to algebraic functions of cyclotomic type, and
(2)Gave determinantal expressions of addition formulae for Abelian functions associated to higher genus algebraic curves,
Hence, we aimed to investigate these results deeply as follows :
(1)should be improved by connecting the result to application on L-series as in the case of Bernoulli, and Hurwitz numbers;
(2)should be generalized to non-hyperelliptic curves.
The results :
The problem (1)is so difficult. We only preparated a manuscript to submit a academic journal. We, however, made a big progress on (2), and published a lot of papers as included in this report.
(1)is needed to investigate further ;
(2)is only proved by a dedious way, and should be proved more directly.
We will continue to research on these problem.
Finally, we hope our results be good hints for researchers who are interesting on theory of Abelian functions.
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Research Products
(13 results)
