The Power-Moments of Polynomial Kloosterman Sums (mod P)

Abstract

在古典的情況下，我們已知classical Kloosterman sum 之k次power-moment 當k最多為4時明顯的公式。在這篇論文中，我們探討polynomial Kloosterman sum和它對應的power-moment。當有限體的特徵值為奇數時，我們得到跟古典情況下類似的公式，而在有限體的特徵值為偶數時，我們也提供在多項式情況下明顯的公式。For the classical Kloosterman sums, it is known the explicit formulas of the k-th power-moment for k being at most 4. In this thesis, we explore the polynomial Kloosterman sums and the corresponding power-moments. When the characteristic of the finite field is odd, the explicit formulas analogous to the formulas in the classical case are given. Moreover, we also provide the explicit formulas in the polynomial case when the characteristic of the finite field is 2.