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Gauss Sums forO(2n+1,q)

✍ Scribed by Dae San Kim

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 354 KB
Volume: 4
Category: Article
ISSN: 1071-5797
DOI: 10.1006/ffta.1997.0202

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✦ Synopsis

For a nontrivial additive character and a multiplicative character of the finite field with q elements (q is a power of an odd prime), the ''Gauss'' sum (tr w) over w3SO(2n#1, q) and (det w) (tr w) over w3O(2n#1, q) are considered. We show that both of them are constant multiples of the sum (tr w) over w3Sp(2n, q), which is, according to our previous result, a polynomial in q with coefficients involving powers of the usual Kloosterman sums. As a consequence, we can determine certain ''signed generalized Kloosterman sums over nonsingular symmetric matrices,'' which were previously determined by J. H. Hodges only in the case that one of the two arguments is zero.

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