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Regularization and generalized double shuffle relations for $p$-adic multiple zeta values

Published online by Cambridge University Press:  20 September 2007

Hidekazu Furusho  and
Amir Jafari
Hidekazu Furusho
Affiliation:
Graduate School of Mathematics, Nagoya University, Nagoya, 464-8602, Japan furusho@math.nagoya-u.ac.jp
Amir Jafari
Affiliation:
Mathematics Department, Duke University, Durham, NC 27708, USA amir@math.duke.edu
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Abstract

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We will introduce a regularization for $p$-adic multiple zeta values and show that the generalized double shuffle relations hold. This settles a question raised by Deligne, given as a project in the Arizona Winter School 2002. Our approach is to use the theory of Coleman functions on the moduli space of genus zero curves with marked points and its compactification. The main ingredients are the analytic continuation of Coleman functions to the normal bundle of divisors at infinity and definition of a special tangential base point on the moduli space.

Keywords

$p$-adic multiple zeta valuedouble shuffle relation$p$-adic multiple polylogarithmColeman's $p$-adic integrationiterated integralsstable compactification of the moduli space11G55 (primary)11S80 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 143 , Issue 5 , September 2007 , pp. 1089 - 1107
Copyright
Foundation Compositio Mathematica 2007