✦ LIBER ✦

Gauss sums and multinomial coefficients

✍ Scribed by Paul Thomas Young

Publisher: Elsevier Science
Year: 2004
Tongue: English
Weight: 251 KB
Volume: 106
Category: Article
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2003.11.003

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✦ Synopsis

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.

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