Erik Panzer
Published 2015-12-14Version 1
We generalize the well-known parity theorem for multiple zeta values (MZV) to functional equations of multiple polylogarithms (MPL). This reproves the parity theorem for MZV with an additional integrality statement, and also provides parity theorems for special values of MPL at roots of unity (also known as coloured MZV). We give explicit formulas in depths 2 and 3 and provide a computer program to compute the functional equations.
Comments: 17 pages, supplemented by a list functional equations and a Maple program
Functional equations of polygonal type for multiple polylogarithms in weights 5, 6 and 7
Relations for Multiple Zeta Values and Mellin Transforms of Multiple Polylogarithms
Evaluation of iterated log-sine integrals in terms of multiple polylogarithms
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