| Project/Area Number |
12440004
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Nagoya University |
|---|
Principal Investigator |
MATSUMOTO Kohji Nagoya University, Graduate School of Math., Professor, 大学院・多元数理科学研究科, 教授 (60192754)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
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)
金光 滋 近畿大学, 九州工学部, 教授 (60117091)
金銅 誠之 名古屋大学, 大学院・多元数理科学研究科, 教授 (50186847)
|
|---|
| Project Period (FY) |
2000 – 2002
|
| Project Status |
Completed (Fiscal Year 2002)
|
| Budget Amount *help |
¥13,700,000 (Direct Cost: ¥13,700,000)
Fiscal Year 2002: ¥4,900,000 (Direct Cost: ¥4,900,000)
Fiscal Year 2001: ¥4,100,000 (Direct Cost: ¥4,100,000)
Fiscal Year 2000: ¥4,700,000 (Direct Cost: ¥4,700,000)
|
|---|
| Keywords | Multiple zeta-function / Euler-Zagier sum / Analytic continuation / Hurwitx zeta-function / Ramanujan's formula / Modular relation / Universality / Automorphic L-function / 漸近展開 / Ramanujan formula / 近似関数等式 / Mellin-Barnes formula / universality / Rankin-Selberg L関数 / 多重ガンマ関数 / Riemannゼータ関数 / 普遍性 / 実二次体 |
|---|
| Research Abstract |
(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.
|
