The Hopf algebra of (q)multiple polylogarithms with non-positive arguments (1503.02977v3)

Published 10 Mar 2015 in math.NT

Abstract: We consider multiple polylogarithms in a single variable at non-positive integers. Defining a connected graded Hopf algebra, we apply Connes' and Kreimer's algebraic Birkhoff decomposition to renormalize multiple polylogarithms at non-positive integer arguments, which satisfy the shuffle relation. The q-analogue of this result is as well presented, and compared to the classical case.

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