The Jacobi sums over Galois rings and its absolute values
J. Korean Math. Soc. 2020 Vol. 57, No. 3, 571-583
Published online May 1, 2020
Young Ho Jang
Inha University
Abstract : The Galois ring $\GR$ of characteristic $p^n$ having $p^{mn}$ elements is a finite extension of the ring of integers modulo $p^n$, where $p$ is a prime number and $n,m$ are positive integers. In this paper, we develop the concepts of Jacobi sums over $\GR$ and under the assumption that the generating additive character of $\GR$ is trivial on maximal ideal of $\GR$, we obtain the basic relationship between Gauss sums and Jacobi sums, which allows us to determine the absolute value of the Jacobi sums.
Keywords : Galois rings, characters, Gauss sums, Jacobi sums
MSC numbers : Primary 11L07, 11T23, 11T24
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