2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61505We give generating functions for Gauss sums for finite general linear and unitary groups. For the general linear case only our method of proof is new, but we deduce a bound on Kloosterman sums which is sometimes sharper than Deligne's bound from algebraic geometry.We add a remark on Fourier analysis and make minor revisionsNumber TheoryAlgebraic Geometrytext