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The parity theorem for multiple polylogarithms

Abstract:
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.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1016/j.jnt.2016.08.004

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
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Name:
European Research Council
Grant:
257638
Publisher:
Elsevier
Journal:
Journal of Number Theory More from this journal
Volume:
172
Pages:
93-113
Publication date:
2016-10-08
Acceptance date:
2016-08-30
DOI:
ISSN:
0022-314X
Keywords:
Pubs id:
pubs:580330
UUID:
uuid:cc114deb-7dda-49b0-bd24-77a50aec52cb
Local pid:
pubs:580330
Source identifiers:
580330
Deposit date:
2016-10-03

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