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On Certain Congruences for Gauss Sums


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Title: On Certain Congruences for Gauss Sums
Authors: Washio, Tadashi / Shimaura, Asako / Shiratani, Katsumi
Issue Date: 31-May-1996
Publisher: 長崎大学教育学部
Citation: 長崎大学教育学部自然科学研究報告. vol.55, p.1-8; 1996
Abstract: In this note, certain congruences for Gauss sums over the finite field GF (pf) are studied. Especially, in the case of f = 1, two deductions for the congruence are given as follows: Let p be any odd prime and ω be the Teichmüller character of conductor p. Let ζp be a fixed primitive p-th root of unity. Then for the Gauss sum g(ωr)=∑xmodp ωr(x)ζxp with respect to any Dirichlet character x=ωr with 1≤r≤p-2, two elementary deductions for a congruence…are given by making use of the Stickelberger theorem and by making use of the Kummer congruences together with the Artin-Hasse exponential series, where p means the prime ideal in Qp (ζp) and ϖ denotes a prime element in Qp (ζp) satisfying…
URI: http://hdl.handle.net/10069/32150
ISSN: 0386443X
Type: Departmental Bulletin Paper
Text Version: publisher
Appears in Collections:No. 55

Citable URI : http://hdl.handle.net/10069/32150

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