Research on arithmetic properties of multiple Dirichlet series

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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.