Research on determinantal formulae and Bernoulli-Hurwitz numbers in the theory of Abelian functions

阿贝尔函数理论中的行列式和Bernoulli-Hurwitz数研究

• 批准号: 16540002
• 负责人: ONISHI Yoshihiro
• 金额: $ 2.3万
• 依托单位: Iwate University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540002/
• 关键词: Abelian function; Algebraic function; Algebraic curve; hyperelliptic curve; division polynomial; Frobenius-Stickelberger; Frobenins-Stickelberger; Bernoulli数; Frobenius-Stickelbergerの公式; Bernoulli-Hurwitz数; 普遍Bernoulli数

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.

感谢科学研究的赠款（C），学年，2000-2002，主题为“针对亚伯利亚功能的特殊价值的产品公式的研究”，首席调查员（Y.O）取得了两个进展：（1）bernoulli-hurwitz数量良好，可为更高的统一功能提供了与cyclotomic类型相关的（2）的综合功能，并获得了（2）的（2）的作用。因此，代数曲线，我们旨在深入研究这些结果，如下所示：（1）应通过将结果连接到伯努利（Bernoulli）和赫维兹（Bernoulli）数字（2）应将其推广到非杂交曲线（2）的结果来改进。我们只准备一份手稿以提交学术期刊。但是，我们在（2）上取得了很大的进展，并发表了许多论文。（1）需要进一步研究；（2）只能通过一种刺激的方式证明，并应更直接地证明我们将继续研究这些问题。我们希望我们的结果是对亚伯里亚功能理论有趣的研究人员的好提示。

项目成果

Determinantal Expressions in hyperelliptic functions(with an Appendix by S.Matsutani)

超椭圆函数中的行列式（附有 S.Matsutani 的附录）

• 期刊: Proceedings of Edinburgh Math.Soc. 未定
• 作者: V.Z.Enolskii;S.Matsutani;Y.Onishi;Y.Onishi;Y.Onishi;Y.Onishi;Yoshihiro Onishi
• 通讯作者: Yoshihiro Onishi

円分型台数函数版Bernoulli-Hurwitz数と普遍Bernoulli数の理論

圆除型伯努利-赫尔维茨数和通用伯努利数的理论

• 发表时间: 2005
• 期刊: 2004数論セミナー静岡報告集
• 作者: V.Z.Enolskii;S.Matsutani;Y.Onishi;大西 良博
• 通讯作者: 大西 良博

Determinant Expressions for purely pentagonal curves of degree six

六次纯五边形曲线的行列式

• 发表时间: 2007
• 期刊: http://arxiv.org/org/abs/math.NT/
• 作者: Shiga;H.;大西良博;Yoshihiro Onishi
• 通讯作者: Yoshihiro Onishi

Determinant expressions for hyperelliptic functions (with an Appendix by S. Matsutani)

超椭圆函数的行列式（附有 S. Matsutani 的附录）

• 发表时间: 2005
• 期刊: Proc. of Edinburgh Math. Soc 48
• 作者: J.C.Eilbeck;V.Z.Enolskii;S.Matsutani;Y.Onishi;E.Peviato;Yoshihiro Onishi
• 通讯作者: Yoshihiro Onishi

Theory of generalized Bernoulli-Hurwitz numbers for algebraic functions of cyclotomic type and universal Bernoulli numbers

分圆型代数函数的广义伯努利-赫尔维茨数理论和通用伯努利数

• 期刊: http://arxiv.org/abs/math.NT/0406096
• 作者: V.Z.Enolskii;S.Matsutani;Y.Onishi;Y.Onishi
• 通讯作者: Y.Onishi