Gauss sum for the adjoint representation of and
We show that for almost all , the inequalityhas solutions with odd prime numbers and , provided . Moreover, we give a rather sharp bound for the exceptional set.This result provides almost-all results for Goldbach numbers in sequences rather thinner than the values taken by any polynomial.
We present a method of bounding incomplete character sums for finite abelian groups with arguments produced by a first-order recursion. This method is particularly effective if the recursion involves a special type of permutation called an -orthomorphism. Examples of -orthomorphisms are given.