Korean J. Math.  Vol 26, No 3 (2018)  pp.519-535
DOI: https://doi.org/10.11568/kjm.2018.26.3.519

The Gauss sums over Galois rings and its absolute values

Young Ho Jang, Sang Pyo Jun

Abstract


Let ${\mathcal R}$ denote the Galois ring of characteristic $p^n$, where $p$ is a prime. In this paper, we investigate the elementary properties of Gauss sums over ${\mathcal R}$ in accordance with conditions of characters of Galois rings, and we restate results for Gauss sums in [1, 2, 3, 7, 12, 13]. Also, we compute the modulus of the Gauss sums.


Keywords


Galois ring, characters of Galois rings, Gauss sums over Galois rings

Subject classification

11T24, 16L60, 42A38, 42B10

Sponsor(s)

Funding for this paper was provided by Namseoul University.

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