Gauss sums and multinomial coefficients

JOURNAL OF NUMBER THEORY

卷:106

Article

Young, PT

关键词: Gauss sums;    multinomial coefficients;    imaginary quadratic fields;   

DOI  :  10.1016/j.jnt.2003.11.003

来源: Elsevier

【 摘 要 】

Consider a Gauss sum for a finite field of characteristic p, where p is an odd prime. When Such a sum (or a product Of Such sums) is a p-adic integer we show how it can be realized as a p-adic limit of a sequence Of multinomial coefficients. As an application we generalize some congruences of Hahn and Lee to exhibit p-adic limit formulae, in terms of multinomial coefficients, for certain algebraic integers in imaginary quadratic fields related to the splitting of rational primes. We also give an example illustrating how Such congruences arise from a p-integral formal group law attached to the p-adic unit part of a product of Gauss Sums. (C) 2003 Elsevier Inc. All rights reserved.

【 授权许可】

Free