Gauss sums and Kloosterman sums over residue rings of algebraic integers期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Gauss sums and Kloosterman sums over residue rings of algebraic integers

Authors:	Ronald Evans

Institution:	Department of Mathematics, University of California at San Diego, La Jolla, California 92093-0112

Abstract:	Let $\mathcal{O}$ denote the ring of integers of an algebraic number field of degree which is totally and tamely ramified at the prime . Write $\zeta_q= \exp(2\pi i/q)$ , where . We evaluate the twisted Kloosterman sum $\begin{displaymath}\sum\limits_{\alpha\in(\mathcal{O}/q \mathcal{O})^} \chi(N(\alpha)) \zeta_q^{T(\alpha)+z/N(\alpha)},\end{displaymath}$ where and denote trace and norm, and where $\chi$ is a Dirichlet character (mod ). This extends results of Salié for and of Yangbo Ye for prime dividing Our method is based upon our evaluation of the Gauss sum $\begin{displaymath}\sum\limits_{\alpha\in (\mathcal{O}/q\mathcal{O})^} \chi(N(\alpha)) \zeta_q^{T(\alpha)},\end{displaymath}$ which extends results of Mauclaire for .

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