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A Dimension Conjecture for q-Analogues of Multiple Zeta Values

  • Henrik BachmannEmail author
  • Ulf Kühn
Conference paper
  • 38 Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 314)

Abstract

We study a class of q-analogues of multiple zeta values given by certain formal q-series with rational coefficients. After introducing a notion of weight and depth for these q-analogues of multiple zeta values we present dimension conjectures for the spaces of their weight- and depth-graded parts, which have a similar shape as the conjectures of Zagier and Broadhurst-Kreimer for multiple zeta values.

Keywords

Multiple zeta values q-Analogues of multiple zeta values Modular forms Dimension conjecture 

Notes

Acknowledgements

We would like to thank N. Matthes and the referees for their careful reading of our manuscript and their valuable comments. The first author would also like to thank the Max-Planck Institute for Mathematics in Bonn for hospitality and support.

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Graduate School of MathematicsNagoya UniversityNagoyaJapan
  2. 2.Universität Hamburg Fachbereich MathematikHamburgGermany

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