Generalized log sine integrals and the Mordell-Tornheim zeta values

Abstract

We introduce certain integrals of a product of the Bernoulli polynomials and logarithms of Milnor’s multiple sine functions. It is shown that all the integrals are expressed by the Mordell-Tornheim zeta values at positive integers and that the converse is also true. Moreover, we apply the theory of the integral to obtain various new results for the Mordell-Tornheim zeta values.