A note on the sign (unit root) ambiguities of Gauss sums in index 2 and 4 cases

Details A note on the sign (unit root) ambiguities of Gauss sums in index 2 and 4 cases A note on the sign (unit root) ambiguities of Gauss sums in index 2 and 4 cases

2009-12-08

arxiv.org/abs/0912.1414v1

Mathematics

Number Theory

Scientific paper

Recently, the explicit evaluation of Gauss sums in the index 2 and 4 cases have been given in several papers (see [2,3,7,8]). In the course of evaluation, the sigh (or unit root) ambiguities are unavoidably occurred. This paper presents another method, different from [7] and [8], to determine the sigh (unit root) ambiguities of Gauss sums in the index 2 case, as well as the ones with odd order in the non-cyclic index 4 case. And we note that the method in this paper are more succinct and effective than [8] and [7].

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