Asymptotic behaviors of the real-analytic Eisenstein series
| Project/Area Number |
20540027
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Nihon University |
|---|
Principal Investigator |
NODA Takumi Nihon University, 工学部, 准教授 (10350034)
|
|---|
| Project Period (FY) |
2008 – 2010
|
| Project Status |
Completed (Fiscal Year 2010)
|
| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
|
|---|
| Keywords | Eisenstein / 級数 / 漸近挙動 / Eisenstein級数 / ゼータ関数 / L-関数 / 漸近展開 / 多重ゼータ関数 / 多重Eisenstein級数 / 積分変換 / 凸性評価 |
|---|
| Research Abstract |
Let E (k ; s ; z) be the non-holomorphic Eisenstein series with an even weight k attached to the modular group SL(2, Z). Our first main achievement of the present project is to establish the uniform asymptotic expansion of E (0 ; s ; z) respect to Im (s), which gives the convexity theorem under some conditions. Our second main achievement is to establish its complete asymptotic expansion as Im (z) to infinity, which gives the another proof of the Fourier series expansion and its applications.
|
Report
(4 results)
Research Products
(34 results)
