Research on analytic properties of multiple Dirichlet series and its application to number theory

研究代表通过与Kohji松本教授（名古屋大学）的合作，建立了与根系相关的多种zeta功能的基础。和Yasushi Komori（Rikkyo Univ.）。此外，在松本的工作基础上，我们得到了一个双zeta函数的函数方程，它可以看作是Riemann zeta函数的一个双重类比。此外，他研究了双重狄利克雷级数的爱森斯坦型涉及双曲函数，并给出了一些公式，他们在正整数。

The research representative established the foundation of the multiple zeta-functions associated with root systems through the joint work with Professors Kohji Matsumoto (Nagoya Univ.) and Yasushi Komori (Rikkyo Univ.). Moreover, based on Matsumoto's previous work, we obtained a functional equation of the double zeta-function which can be regarded as a double analogue of that of Riemann's zeta-function. In addition, he studied double Dirichlet series of Eisenstein type involving hyperbolic functions, and gave some formulas for them at positive integers.