On certain character sums over p-adic rings and their L-functions

被引：2

作者：

Blache, Regis ^{[1
]}

机构：

[1] Univ Polynesie Francaise, Equipe Geometrie Algebr & Applicat Theorie Inform, BP 6570, Faaa 98702, Tahiti, France

来源：

MATHEMATISCHE NACHRICHTEN | 2007年 / 280卷 / 15期

关键词：

p-adic character sums; L-functions; Gauss sums; Weil numbers;

D O I：

10.1002/mana.200510571

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we present a new method for evaluating exponential sums associated to a restricted power series in p(l) one variable modulo p, a power of a prime. We show that for sufficiently large l, these sums can be expressed in terms of Gauss sums. Moreover, we study the associated L-functions; we show that they are rational, then we determine their degrees and the weights as Weil numbers of their reciprocal roots and poles. (C) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

引用

页码：1681 / 1697

页数：17

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