臺灣博碩士論文加值系統

在這篇論文裡,我們計算橢圓曲線上局部系統的拉普拉斯算子的特 徵值與特徵方程式,我們也計算正規光譜 zeta 函數和其相對應的曲線 上平坦線叢的拉普拉斯算子的解析 torsion 。

In this paper, we determine the eigenvalues and eigenfunctions of the Laplacian on local systems over elliptic curves X. We will also compute the regularized spectral zeta function and the corresponding analytic torsion of the Laplacian of a flat line bundle on the curve X.

1. Introduction 1
2. Fourier Series on Tori 3
3. Sheaf 5
4. Line bundle and Picard Group 6
5. Eigenvalues and Eigenfunctions Problems 9
6. Regularized spectral zeta function and analytic torsion 12
References 18

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[2] J. Morrow and K. Kodaira, Complex Manifolds, Holt, Rinehart and Winston, New York, 1971.
[3] D. B. Ray and I. M. Singer, Analytic Torsion for Complex Manifolds, Annals of Mathematics, Second Series, Vol. 98, No.1, pp. 154-177, Jul., 1973.
[4] C. L. Siegel, Lectures on advanced analytics number theory, Tata In- stitute, Bombay, 1961.