Zeta-functions and special functions

Zeta 函数和特殊函数

基本信息

批准号：
17540050
负责人：
KANEMITSU Shigeru
金额：
$ 2.46万
依托单位：
Kinki University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2005
资助国家：
日本
起止时间：
2005 至 2007
项目状态：
已结题

项目摘要

In these three years, I have been working on the equivalent forms of the functional equations for the zeta-functions. We have made it clear that the essential ingredient in the equivalent forms is the Fox H-functions and we have succeeded in formulating the most general form of the modular relation which is expected to be applied to various fields where the zeta-functions appear. We have also revealed that many of the existing relations that look independent of the functional equation are indeed, disguised form thereof typically, the partial fraction expansion for the cotangent function is one.In the cited papers which are published in 2006, we have presented various aspects of the modular relation. Especially, in aspects we have interpreted the functional equation of the Hurwitz-Lerch zeta-function as a manifestation of the modular relation. In applications we have made an essential use of the Fox H-functions to give all possible equivalent assertions to the functional equation (with … More gamma factor appearing on one side only) in the form of the modular relation.In 2007 I have published one book and one proceedings volume. The book is coauthored by the joint researcher Dr. Tsukada, and we state it as an achievement. The contents are as follows. Through the theory of zeta-functions, we may develop the new construction of the theory of special functions including Bernoulli polynomials, gamma function. It also contains the theory of Epstein zeta-functions and its applications to ionic crystals as well as the theory of the Dirichlet L-functions and its applications to class number formulas. The second is the proceedings of the 4?th China-Japan Seminar on number theory-Sailing on the sea of number theory, which contains far-reaching survey papers ranging from analytic number theory to algebraic number theory and is intended for breeding the new generations in both Japan and China. This happens to be Vol. 2 of the book series “Number Theory and its Applications" which the reporter has been editing. In 2007 Vol. 4, by M. Hata has appeared, “Problems in analysis" which contains worked-out problems in analysis and related fields.In 2007 there appeared two papers. One is about the Hurwitz zeta-function in which we give a proof based on the difference equation satisfied by it to prove Ramanujan's formula which in turn can compress 215 pages of the book by Srivastava and Choi, and as a whole constitutes the culmination of the studies in this direction. Less

在这三年中，我一直在Zeta功能的功能方程式上，等效形式是fox h功能，我们一直在提出最通用的thich形式。看起来独立于功能方程式确实是在2006年发表的引用论文的扩展，我们在模块化关系的各个方面都呈现了各个方面。 ATH是模块化关系的一种模块化关系（仅出现在一侧），以模块化关系的形式出现。通过zeta函数的理论，我们可以发展出bernoulli polylli的新结构，即dirichlet l功能的理论，并且是第二个公式。并且是“记者一直在编辑的应用程序。HATA出现了，“分析问题”，其中包含有效的分析和相关领域的问题。反过来，Srivastava和Choi可以压缩215本书的书，并且作为整个研究的顶点。

项目成果

期刊论文数量（0）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Structural elucidation of teh mean square of the Hurwits seta-function

Hurwits seta 函数的均方结构解析

DOI：
发表时间：
2006
期刊：
J. Number Theory 120
影响因子：
0
作者：
金光滋;谷川好男;吉元昌己
通讯作者：
吉元昌己

On the partial fraction expansion for the cotangent function

关于余切函数的部分分数展开式

DOI：
发表时间：
2007
期刊：
Proc. of the conference in honor of Prof. Ramachandra
影响因子：
0
作者：
R.Balasubramanian;L.-P.Ding;金光滋;谷川好男
通讯作者：
谷川好男

Some number-theoretic applications of a general modular relation

一般模关系的一些数论应用

DOI：
发表时间：
2006
期刊：
Intern.J.Number Theory 2
影响因子：
0
作者：
R.Balasubramanian;L.-P.Ding;金光滋;谷川好男;T. Akita and N. Kawazumi;金光滋
通讯作者：
金光滋

On a generalization of the Demyanenko determinant

关于 Demyanenko 行列式的推广

DOI：
发表时间：
2007
期刊：
Abh.Math.Sem.Univ.Hamburg 77
影响因子：
0
作者：
Mikihito Hirabayashi;Hirofumi Tsumura;Mikihito Hirabayashi;Toshiyuki Akita;Toshiyuki Akita;金光滋;T. Akita and N. Kawazumi;S. Kanemitsu;金光滋
通讯作者：
金光滋

Some Aspects of the Modular Relation