The parity theorem for multiple polylogarithms

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• 作者：Erik Panzer ^{erik.panzer@all-souls.ox.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Multiple zeta values ; Multiple polylogarithms ; Coloured MZV ; Parity theorem ; Generalized parity ; Roots of unity ; Functional equation
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：172
• 期：Complete
• 页码：93-113
• 全文大小：481 K

文摘

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.