TANIGAWA Yoshio Nagoya University, Graduate School of Math., Assoc.Prof., 大学院・多元数理科学研究科, 助教授 (50109261)
KATSURADA Masanori Keio Univ., Fac.of Econ., Professor, 経済学部, 教授 (90224485)
KITAOKA Yoshiyuki Meijo Univ., Fac.of Sci.& Tech., Professor, 理工学部, 教授 (40022686)
AKIYAMA Shigeki Niigata Univ., Fac.of Sci., Assoc.Prof., 理学部, 助教授 (60212445)
KIUCHI Isao Yamaguchi Univ., Fac.of Sci., Assoc.Prof., 理学部, 助教授 (30271076)
(1) We introduced the notion of generalized multiple zeta-functions, which is a generalization of both the Euler-Zagier multiple sums and the Barnes multiple zeta-functions, and, by using the Mellin-Barnes integral formula, proved their analytic continuation and asymptotic expansions. As applications, we proved asymptotic expansions of higher power moments of Hurwitz zeta-functions, and also explicit formulas of determinants of the Laplacians of high-dimensional spheres.
(2) We found a basic principle connecting Ramanujan's formula, modular relations, and approximate functional equations, and proved rapidly converget series expressions of various L-functions, in connection with multiple zeta-functions.
(3) We introduced the positive density method in universality theory, and proved the universality of automorphic L-functions, and Rankin-Selberg L-fanctions, attached to cusp forms of SL (2, II) or its congruence sabgroups, also the joint universality of Lerch zeta-functions.