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

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Published: Sep 30, 2018
Keywords:
Galois ring, characters of Galois rings, Gauss sums over Galois rings
Mathematics Subject Classification:
11T24, 16L60, 42A38, 42B10

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Young Ho Jang
Department of Mathematics Inha University Incheon, 22212, Korea
Sang Pyo Jun
Information Communication Namseoul University Chun-An 31020, Korea

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.



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Supporting Agencies

Funding for this paper was provided by Namseoul University.

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