| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2009: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2007: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
|---|
| Research Abstract |
Let $E_k(s;z)$ be the non-holomorphic Eisenstein series with an even weight $k$ attached to the modular group $SL_2({\mathbb{Z})$. One of the major achievements of the present project is to establish its complete asymptotic expansion as $\Im z\to+\infty$ ; this yields various useful results on $E_k(s;z)$, which include its asymptotic expansion as $z\to0$ through the sector $0<\arg z<\pi$, its Fourier series expansion, and further the direct proof that it becomes the eigenfunction of the non-Euclidean Laplacian of weight $k$.
|
