Gamma-function and Gaussian-sum-function
After some remarks about the analogy between the classical gamma-function and Gaussian sums over finite fields a complete, very short explicit proof is given of an identity expressing a certain sum of products of Gaussian sums as a product of Gaussian sums. This identity is an analogue of the classical Barnes’ first lemma for the gamma-function. Four multiplicative characters of a finite field are concerned; the usually necessary restrictions on the triviality of certain products of these characters...