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On relations for the multiple q-zeta values

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Abstract

We prove a new relation for the multiple q-zeta values (MqZV’s). It is a q-analogue of the Ohno-Zagier relation for the multiple zeta values (MZV’s). We discuss the problem of determining the dimension of the space spanned by MqZV’s over ℚ, and present an application to MZV.

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References

  1. Bradley, D.M.: Multiple q-zeta values. J. Algebra 283(2), 752–798 (2005). Preprint: February 6, 2004, http://arxiv.org/abs/math.QA/0402093

    Article  MATH  MathSciNet  Google Scholar 

  2. Gasper, G., Rahman, M.: Basic Hypergeometric Series. Encyclopedia of Mathematics and its Applications, vol. 35. Cambridge University Press, Cambridge (1990). With a foreword by Richard Askey

    MATH  Google Scholar 

  3. Hoffman, M.E., Ohno, Y.: Relations of multiple zeta values and their algebraic expression. J. Algebra 262(2), 332–347 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  4. Kaneko, M.: Private communications (2004)

  5. Ohno, Y.: A generalization of the duality and sum formulas on the multiple zeta values. J. Number Theory 74(1), 39–43 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  6. Ohno, Y., Zagier, D.: Multiple zeta values of fixed weight, depth, and height. Indag. Math. (N.S.) 12(4), 483–487 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  7. Terasoma, T.: Mixed Tate motives and multiple zeta values. Invent. Math. 149(2), 339–369 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  8. Zagier, D.: Values of zeta functions and their applications. In: First European Congress of Mathematics, vol. II, Paris, 1992. Progr. Math., vol. 120, pp. 497–512. Birkhäuser, Basel (1994)

    Google Scholar 

  9. Zhao, J.: q-Multiple zeta functions and q-multiple polylogarithms. Preprint, May 23 (2003). http://arxiv.org/abs/math.QA/0304448

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Authors and Affiliations

  1. Department of Mathematical Sciences, Science and Engineering, Waseda University, Tokyo, 169-8555, Japan

    Jun-ichi Okuda

  2. Graduate School of Pure and Applied Sciences, University of Tsukuba, Ibaraki, 305-8571, Japan

    Yoshihiro Takeyama

Authors
  1. Jun-ichi Okuda
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  2. Yoshihiro Takeyama
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Corresponding author

Correspondence to Jun-ichi Okuda.

Additional information

The first author is supported by Grant-in-Aid for Young Scientists (B) No. 17740026 and the second author is supported by Grant-in-Aid for Young Scientists (B) No. 17740089.

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Okuda, Ji., Takeyama, Y. On relations for the multiple q-zeta values. Ramanujan J 14, 379–387 (2007). https://doi.org/10.1007/s11139-007-9053-5

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  • DOI: https://doi.org/10.1007/s11139-007-9053-5

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