ON THE MEAN SQUARE AVERAGE OF DIRICHLET L-FUNCTION OVER CHARACTERS OF ODD PARITY IN A SPECIAL CASE

摘要

Evaluating the mean square averages of the Dirichlet L-functions over Dirichlet char-acters chi of the same parity is an active problem in number theory. Here we explicitly evaluate E chi odd L(3, chi) using certain trigonometric sums and Bernoulli polynomials and express the sum in terms of the Euler totient function phi and the Jordan totient function Js.