Study of modular varieties and modular forms

模块化品种和模块化形式的研究

• 批准号: 20540026
• 负责人: HAMAHATA Yoshinori
• 金额: $ 1.75万
• 依托单位: Tokyo University of Science
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20540026/
• 关键词: 数論; ベルヌーイ数; ゼータ関数; デデキント和; Dedekind和; Bernoulli多項式; 保型形式

We investigated poly-Bernoulli polynomials, Arakawa-Kaneko zeta functions, and Dedekind sums in finite characteristic. T. Arakawa and M. Kaneko introduced a certain zeta function, which is called the Arakawa-Kaneko zeta function, to clarify the relation between multiple zeta values and poly-Bernoulli numbers. A. Bayad and I introduced and studied poly-Bernoulli polynomials and the Arakawa-Kaneko zeta function of Hurwitz type. Our result was published in Kyushu J. Math. in 2011. After that, we extended our Bernoulli polynomials and the zeta function into two directions. These can be applicable. We reported a part of our results at RIMS workshop in 2010. We next report the results about the Dedekind sums. The Dedekind sums were introduced by Dedekind to describe the transformation formula of the Dedekind eta-function. These sums have many applications. Zagier gave a higher dimensional version of these sums. We have investigated the Dedekind sums in finite characteristic. We introduced higher dimensional Dedekind sums, and established the reciprocity law, rationality, and the Knopp identity. Moreover, we introduced the generalized higher dimensional Dedekind sums, and described the values of L-functions in terms of the Dedekind sums.

我们研究了多伯努利多项式，Arakawa-Kaneko zeta函数和有限特征的Dedekind和。T. Arakawa和M. Kaneko引入了一种zeta函数，称为Arakawa-Kaneko zeta函数，以阐明多重zeta值与poly-Bernoulli数之间的关系。A. Bayad和我介绍并研究了多伯努利多项式和Hurwitz型的Arakawa-Kaneko zeta函数。我们的结果发表在2011年的Kyushu J. Math.上。在此之后，我们将我们的伯努利多项式和zeta函数扩展到两个方向。这些可以适用。我们在2010年的RIMS研讨会上报告了我们的部分结果。我们接下来报告有关戴德金和的结果。Dedekind引入Dedekind和来描述Dedekind eta函数的变换公式。这些和有许多应用。Zagier给了一个高维版本的这些款项。研究了有限特征的Dedekind和。我们引入了高维Dedekind和，建立了互反律、合理性和Knopp恒等式。引入了广义高维Dedekind和，并利用Dedekind和刻画了L-函数的值。

项目成果

Multiple polylogarithms and multi-poly-Bernoulli polynomials

多重多项式和多重伯努利多项式

• 期刊: Functiones et Approximatio Commentarii Mathematici
• 影响因子: 0.5
• 作者: A.Bayad;浜畑芳紀
• 通讯作者: 浜畑芳紀

POLYLOGARITHMS AND POLY-BERNOULLI POLYNOMIALS

• DOI: 10.2206/kyushujm.65.15
• 发表时间: 2011-03
• 期刊: Kyushu Journal of Mathematics
• 影响因子: 0.4
• 作者: A. Bayad;Y. Hamahata

Higher dimensional Dedekind sums in finite fields

有限域中的高维戴德金和

• 期刊: Finite Fields and Their Applications
• 影响因子: 1
• 作者: A.Bayad;浜畑芳紀
• 通讯作者: 浜畑芳紀

Dedekind sums in finite characteristic

有限特征中的戴德金求和

• 发表时间: 2008
• 期刊: Proceedings of the Japan Academy 84
• 作者: A.Bayad;Y.Hamahata;浜畑芳紀
• 通讯作者: 浜畑芳紀

Arakawa–Kaneko L-functions and generalized poly-Bernoulli polynomials

Arakawa–Kaneko L 函数和广义聚伯努利多项式

• DOI: 10.1016/j.jnt.2010.11.005
• 发表时间: 2011
• 期刊: Journal of Number Theory
• 影响因子: 0.7
• 作者: A. Bayad;Y. Hamahata
• 通讯作者: Y. Hamahata