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Mathematische Zeitschrift

, Volume 290, Issue 3–4, pp 1173–1197 | Cite as

Checkerboard style Schur multiple zeta values and odd single zeta values

  • Henrik Bachmann
  • Yoshinori Yamasaki
Article
  • 197 Downloads

Abstract

We give explicit formulas for the recently introduced Schur multiple zeta values, which generalize multiple zeta(-star) values and which assign to a Young tableaux a real number. In this note we consider Young tableaux of various shapes, filled with alternating entries like a Checkerboard. In particular we obtain new sum representation for odd single zeta values in terms of these Schur multiple zeta values. As a special case we show that some Schur multiple zeta values of Checkerboard style, filled with 1 and 3, are given by determinants of matrices with odd single zeta values as entries.

Keywords

Multiple zeta values Schur functions Jacobi–Trudi formula Hypergeometric functions Hankel determinants 

Mathematics Subject Classification

11M41 05E05 33C05 

Notes

Acknowledgements

The authors would like to thank Don Zagier for his ideas on parts of the proof of Theorem 3.5, Wadim Zudilin for helpful discussion on the topic, Steven Charlton for corrections and calculations in Section 5 and the Max-Planck-Institut für Mathematik in Bonn for hospitality and support.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Graduate School of MathematicsNagoya UniversityNagoyaJapan
  2. 2.Graduate School of Science and EngineeringEhime UniversityEhimeJapan

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