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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.
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참고문헌 (13)
참고문헌 신청
B. C. Berndt / 1998 / Gauss and Jacobi sums, Canadian Mathematical Society Series of Monographs and Advanced Texts / John Wiley & Sons, Inc
S. Fan / 2004 / Character sums over Galois rings and primitive polynomials over nite elds / Finite Fields Appl 10(1):36~52
K. F. Ireland / 1982 / Graduate Texts in Mathematics, 84 / Springer-Verlag
H. Ishibashi / 1996 / The Terwilliger algebras of certain association schemes over the Galois rings of characteristic 4 / Graphs Combin 12(1):39~54
전상표 / 2018 / The Gauss sums over Galois rings and its absolute values / 한국수학논문집 26(3):519~535
S. Fan / 2004 / Character sums over Galois rings and primitive polynomials over nite elds / Finite Fields Appl 10(1):36~52
K. F. Ireland / 1982 / Graduate Texts in Mathematics, 84 / Springer-Verlag
H. Ishibashi / 1996 / The Terwilliger algebras of certain association schemes over the Galois rings of characteristic 4 / Graphs Combin 12(1):39~54
전상표 / 2018 / The Gauss sums over Galois rings and its absolute values / 한국수학논문집 26(3):519~535
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