Investigation of the behaviours of zeta and theta functions from a viewpoint of the theory of multiple hypergeometric functions

从多重超几何函数理论的角度研究 zeta 和 theta 函数的行为

• 批准号: 23540025
• 负责人: KATSURADA Masanori
• 金额: $ 3.24万
• 依托单位: Keio 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-23540025/
• 关键词: 漸近展開; ゼータ関数; 多変数超幾何関数

The following items (1)---(3) describe the major consequences of our study during the fiscal years 2011--2013: (1) it is shown that complete asymptotic expansions exist for the double Shintani zeta-functions defined with $n$ complex variables $\mathbold{s}$ and $n$ complex parameters $\mathbold{z}$ when $\mathbold{z}$ becomes both small and large; (2) it is shown that complete asymptotic expansions exist for the double holomorphic Eisenstein series of two complex variables and with two complex parameters $z_j$ $(j=1,2)$ when the distance $|z_2-z_1|$ of the basis parameters becomes both small and large; (3) Let $q$ be a complex parameter with $|q|<1$. It is then shown that complete asymptotic expansions exist for certain weighted multiple $q$-integrals and $q$-differentials when $q\to1$.

以下（1）-（3）描述了我们在2011- 2013财年期间研究的主要结果：（1）证明了当$\mathbold{z}$变小和变大时，定义为$n$复变量$\mathbold{s}$和$n$复参数$\mathbold {z}$的双重Shintani zeta函数存在完全渐近展开;（2）证明了具有两个复参数z_j（j= 1，2）的两个复变量的二重全纯Eisenstein级数，当距离|z_2-z_1|（3）设q为复参数，|Q| <1美元。然后，它表明，完全渐近展开存在某些加权多重q$-积分和q$-微分时，$q\to 1 $。

项目成果

Shintani zeta-functions of several variables and Lauricella hypergeometric functions II

Shintani zeta 多变量函数和 Lauricella 超几何函数 II

• 发表时间: 2012
• 作者: Takashi ICHIKAWA (Chief);Masanari Kida and Takao Yamazaki (eds.);Masanori Katsurada
• 通讯作者: Masanori Katsurada

Hypergeometric-type generating functions of several variables associaed with the Lerch zeta-function

与 Lerch zeta 函数相关的多个变量的超几何型生成函数

• 作者: N. Suwa;A. Shiho;K. Sato (eds);津村博文;Masanori KATSURADA
• 通讯作者: Masanori KATSURADA

Transformation formulae and asymptotic expansions for double holomorphic Eisenstein series of two variables

二变量双全纯爱森斯坦级数的变换公式和渐近展开式

• 发表时间: 2014
• 作者: Kaneda;M.;Masanori Katsurada;Takashi ICHIKAWA;D. Essouabri and K. Matsumoto and H. Tsumura;Masanori Katsurada and Takumi Noda
• 通讯作者: Masanori Katsurada and Takumi Noda

Asymptotic expansions for certain multiple $q$-integrals and $q$-differentials of Thomae-Jackson type and their applications

某些Thomae-Jackson型多重$q$-积分和$q$-微分的渐近展开及其应用

• 作者: Y.Komori;K.Matsumoto and H. Tsumura;鍬田 政人;Hiroshima Math. J;Masanori Katsurada;M. Katsurada and T. Noda;津村博文;N. Suwa;M. Katsurada and T. Noda;津村博文;M. Katsurada;諏訪紀幸;津村博文;諏訪紀幸;Masanori KATSURADA;諏訪紀幸;津村博文;Masanori KATSURADA
• 通讯作者: Masanori KATSURADA

Complete asymptotic expansions associated with Epstein zeta-functions II (summarized version)

与 Epstein zeta 函数 II 相关的完全渐近展开式（总结版）

• 发表时间: 2012
• 期刊: RIMS K\^oKy\^uroku
• 作者: Y. Komori;K. Matsumoto and H. Tsumura;Masanori KATSURADA
• 通讯作者: Masanori KATSURADA