On multiple higher Mahler measures and Witten zeta values associated with semisimple Lie algebras

The Witten zeta-functions associated with semisimple Lie algebras were defined by Zagier, and their special values at even positive integers were first studied by Witten in connection with quantum gauge theory. In this paper, relations between multiple higher Mahler measures for some families of polynomials and special values of Witten zeta-functions at positive integers are showed. Consequently, a geometrical interpretation of the multiple higher Mahler measure as the volume of certain moduli space is given.

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Published 11 June 2013