Evaluations of a Weighted Average of Gauss Sums - Wen-Kai Shao; Yuan He (Journal of Mathematics)
In this paper, we perform a further investigation for a weighted average of Gauss sums. By making use of some properties of the cotangent function and the Bernoulli polynomials, we explicitly evaluate the weighted average of Gauss sums in terms of the special values of Dirichlet L-functions at positive integers.