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A Restricted Sum Formula for a q-Analogue of Multiple Zeta Values

Conference paper
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Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 40)

Abstract

We prove a new linear relation for a q-analogue of multiple zeta values. It is a q-extension of the restricted sum formula obtained by Eie, Liaw and Ong for multiple zeta values.

Keywords

Multiple Zeta Values (MZV) Harmonic Sums Noncommutative Polynomial Algebra Admissible Indices Article Claims 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The research of the author is supported by Grant-in-Aid for Young Scientists (B) No. 23740119. The author is grateful to Yasuo Ohno for helpful informations.

References

  1. 1.
    Bradley, D.M.: Multiple q-zeta values. J. Algebra 283(2), 752–798 (2005) MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Bradley, D.M.: On the sum formula for multiple q-zeta values. Rocky Mt. J. Math. 37(5), 1427–1434 (2007) zbMATHCrossRefGoogle Scholar
  3. 3.
    Eie, M., Liaw, W., Ong, Y.L.: A restricted sum formula among multiple zeta values. J. Number Theory 129(4), 908–921 (2009) MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Granville, A.: A decomposition of Riemann’s zeta-function. In: Analytic Number Theory, Kyoto, 1996. London Math. Soc. Lecture Note Ser., vol. 247, pp. 95–101. Cambridge Univ. Press, Cambridge (1997) CrossRefGoogle Scholar
  5. 5.
    Kaneko, M., Kurokawa, N., Wakayama, M.: A variation of Euler’s approach to values of the Riemann zeta function. Kyushu J. Math. 57(1), 175–192 (2003) MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Ohno, Y., Zagier, D.: Multiple zeta values of fixed weight, depth, and height. Indag. Math. 12(4), 483–487 (2001) MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Okuda, J., Takeyama, Y.: On relations for the multiple q-zeta values. Ramanujan J. 14(3), 379–387 (2007) MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Takeyama, Y.: Quadratic relations for a q-analogue of multiple zeta values. Ramanujan J. 27(1), 15–28 (2012) MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Zagier, D.: Multiple zeta values. Unpublished manuscript (1995) Google Scholar
  10. 10.
    Zhao, J.: Multiple q-zeta functions and multiple q-polylogarithms. Ramanujan J. 14(2), 189–221 (2007) MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.Division of Mathematics, Faculty of Pure and Applied SciencesUniversity of TsukubaTsukuba, IbarakiJapan

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