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

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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.