Gauss sums for U(2n, q2)
Dae San Kim · Glasgow Mathematical Journal · 1998
Abstract 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.