The parity theorem for multiple polylogarithms

JOURNAL OF NUMBER THEORY

卷:172

Article

Panzer, Erik¹ 

[1] All Souls Coll, Oxford OX1 4AL, England

关键词: Multiple zeta values;    Multiple polylogarithms;    Coloured MZV;    Parity theorem;    Generalized parity;    Roots of unity;    Functional equation;   

DOI  :  10.1016/j.jnt.2016.08.004

来源: Elsevier

【 摘 要 】

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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free