Analytic continuation of multiple polylogarithms

Abstract

In this paper we shall define the analytic continuation of the multiple polylogarithms by using Chen's theory of iterated path integrals and compute the monodromy of all multiple logarithms explicitly.

16 pages, a sign error corrected

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• Alternating Multiple Mixed Values: Regularization, Special Values, Parity and Dimension Conjectures
• Analytic continuation of multiple polylogarithms in positive characteristic
• Explicit Relations of Some Variants of Convoluted Multiple Zeta Values
• Analytic continuation of Kochubei multiple polylogarithms and its applications
• Explicit Evaluation of Euler-Apéry Type Multiple Zeta Star Values and Multiple $t$-Star Values