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Letters in Mathematical Physics

, Volume 106, Issue 3, pp 365–380 | Cite as

Renormalisation of q-Regularised Multiple Zeta Values

  • Kurusch Ebrahimi-Fard
  • Dominique Manchon
  • Johannes Singer
Article

Abstract

We consider a particular one-parameter family of q-analogues of multiple zeta values. The intrinsic q-regularisation permits an extension of these q-multiple zeta values to negative integers. Renormalised multiple zeta values satisfying the quasi-shuffle product are obtained using an Hopf-algebraic Birkhoff factorisation together with minimal subtraction.

Keywords

multiple zeta values renormalisation Hopf algebra q-analogues quasi-shuffle relation 

Mathematics Subject Classification

11M32 16T05 

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Kurusch Ebrahimi-Fard
    • 1
  • Dominique Manchon
    • 2
  • Johannes Singer
    • 3
  1. 1.ICMATMadridSpain
  2. 2.Univ. Blaise Pascal, CNRS, UMR 6620AubièreFrance
  3. 3.Department MathematikFriedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany

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