Research on arithmetic properties of multiple Dirichlet series

多重Dirichlet级数算术性质研究

• 批准号: 23540022
• 负责人: TSUMURA Hirofumi
• 金额: $ 3.16万
• 依托单位: Tokyo Metropolitan University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23540022/
• 关键词: 代数学; 整数論; ゼータ関数; 解析数論・フランス

We study analytic properties of the multiple Dirichlet series from the various viewpoints. In particular, we obtain some value-relations and functional relations for them, and consider their applications to number theory. Concretely we study Witten's zeta-functions associated with the root systems and certain Eisenstein type series as a joint work with K. Matsumoto (Nagoya University) and Y. Komori (Rikkyo University). Our research is being completed as a fruitful theory. As for double zeta-functions, we obtain a new type of the mean value theorem. We greatly expect its application to number theory.

从不同的角度研究了多重Dirichlet级数的解析性质。特别地，我们得到了它们的一些值关系和函数关系，并考虑了它们在数论中的应用。具体地说，我们与K.MatSumoto(名古屋大学)和Y.Komori(Rikkyo大学)合作，研究了与根系有关的Witten Zeta函数和某些Eisenstein型级数。我们的研究正在完成，成为一个富有成果的理论。对于双Zeta函数，我们得到了一种新的中值定理。我们非常期待它在数论中的应用。

项目成果

Analogues of level-N Eisenstein series

N级爱森斯坦系列的类似物

• 发表时间: 2012
• 期刊: Pacific J. Math
• 作者: Y. Komori;K. Matsumoto and H. Tsumura;Yasuro Gon;H. Tsumura
• 通讯作者: H. Tsumura

Evaluation formulas of Cauchy-Mellin type for certain series involving hyperbolic functions

某些涉及双曲函数的级数的Cauchy-Mellin型评价公式

• 发表时间: 2011
• 期刊: Comment. Math. Univ. St. Pauli
• 作者: Y. Komori;K. Matsumoto and H. Tsumura
• 通讯作者: K. Matsumoto and H. Tsumura

A study on multiple zeta values from the viewpoint of zeta-functions of root systems

• DOI: 10.7169/facm/2014.51.1.3
• 发表时间: 2012-05
• 期刊: arXiv: Number Theory
• 作者: Y. Komori;Kohji Matsumoto;Hirofumi Tsumura

ON WITTEN MULTIPLE ZETA-FUNCTIONS ASSOCIATED WITH SEMI-SIMPLE LIE ALGEBRAS IV

• DOI: 10.1007/978-0-8176-8334-4_11
• 发表时间: 2009-07
• 期刊: Glasgow Mathematical Journal
• 影响因子: 0.5
• 作者: Y. Komori;Kohji Matsumoto;Hirofumi Tsumura

Functional relations for zeta-functions of weight lattices of Lie groups of type A_3, in `Analytic and Probabilistic Methods in Number Theory', E. Manstavicius et al. (eds)

A_3 型李群权重格的 zeta 函数的函数关系，参见“数论中的分析和概率方法”，E. Manstavicius 等人。

• 发表时间: 2012
• 期刊: TEV
• 作者: Y. Komori;K. Matsumoto and H. Tsumura
• 通讯作者: K. Matsumoto and H. Tsumura