Geodesic
Gauss sums for U(2n, q2)
Glasgow mathematical journal, Tome 40 (1998) no. 1, pp. 79-95

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Kim, Dae San. Gauss sums for U(2n, q2). Glasgow mathematical journal, Tome 40 (1998) no. 1, pp. 79-95. doi: 10.1017/S0017089500032377
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