Double shuffle relations and renormalization of multiple zeta values

Details Double shuffle relations and renormalization of multiple zeta values Double shuffle relations and renormalization of multiple zeta values

2009-05-30

arxiv.org/abs/0906.0092v1

Mathematics

Number Theory

Scientific paper

In this paper we present some of the recent progresses in multiple zeta values (MZVs). We review the double shuffle relations for convergent MZVs and summarize generalizations of the sum formula and the decomposition formula of Euler for MZVs. We then discuss how to apply methods borrowed from renormalization in quantum field theory and from pseudodifferential calculus to partially extend the double shuffle relations to divergent MZVs.

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