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Gauss sums for U(2n, q2)

Published online by Cambridge University Press:  18 May 2009

Dae San Kim
Dae San Kim
Affiliation:
Department of MathematicsSeoul Women's UniversitySeoul 139–774Korea
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Abstract

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For a lifted nontrivial additive character λ' and a multiplicative character λ of the finite field with q2 elements, the “Gauss” sums Σ λ'(trg) over g ∈SU(2n, q2) and Σ λ (detg)λ'(trg) over g ∈ U(2n, q2) are considered. We show that the first sum is a polynomial in q with coefficients involving averages of “bihyperkloosterman sums” and that the second one is a polynomial in q with coefficients involving powers of the usual twisted Kloosterman sums. As a consequence, we can determine certain “generalized Kloosterman sums over nonsingular Hermitian matrices”, which were previously determined by J. H. Hodges only in the case that one of the two arguments is zero.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 40 , Issue 1 , March 1998 , pp. 79 - 95
Copyright
Copyright © Glasgow Mathematical Journal Trust 1998

References

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