The Jacobi sums over Galois rings and its absolute values
J. Korean Math. Soc. 2020 Vol. 57, No. 3, 571-583
https://doi.org/10.4134/JKMS.j190211
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
Downloads: Full-text PDF   Full-text HTML

   

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd