The Ramanujan Journal

, Volume 47, Issue 3, pp 651–658 | Cite as

On the duality and the derivation relations for multiple zeta values

  • Naho Kawasaki
  • Tatsushi Tanaka


We consider the problem of deducing the duality relation from the extended double shuffle relation for multiple zeta values. Especially we prove that the duality relation for double zeta values and that for the sum of multiple zeta values whose first components are 2’s are deduced from the derivation relation, which is known as a subclass of the extended double shuffle relation.


Multiple zeta values Duality relation Derivation relation Extended double shuffle relation 

Mathematics Subject Classification




The authors express great thanks to Prof. Yasuo Ohno and Prof. Masanobu Kaneko for helpful comments and advice in the MZV conference at Kinki university on Feb., 2017.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematical InstituteTohoku UniversitySendaiJapan
  2. 2.Department of Mathematics, Faculty of ScienceKyoto Sangyo UniversityKyoto-CityJapan

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