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Abstract

We express the mean square value of the Dirichlet L-function at positive integers as a linear combination of its values at even numbers and for a principal character. The method we take is to construct a connection between a special kind of trigonometric functions and the Dirichlet L-function. Since the coefficients of the linear combination satisfy computable recursion formulae, we can obtain the exact mean square value of the Dirichlet L-function using mathematical software.