• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.571-583
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• 2020

The Galois ring R of characteristic pⁿ having p^mn elements is a finite extension of the ring of integers modulo pⁿ, where p is a prime number and n, m are positive integers. In this paper, we develop the concepts of Jacobi sums over R and under the assumption that the generating additive character of R is trivial on maximal ideal of R, we obtain the basic relationship between Gauss sums and Jacobi sums, which allows us to determine the absolute value of the Jacobi sums.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1893-1908
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• 2016

In this paper, we obtain some behaviours of theta sums of higher index for the $Schr{\ddot{o}}dinger$-Weil representation of the Jacobi group associated with a positive definite symmetric real matrix of degree m.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.1-10
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• 2009

Main purpose of this paper is to define an elliptic analogue of the Hardy sums. Some results, which are related to elliptic analogue of the Hardy sums, are given.