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ON MULTIPLE ZETA VALUES OF EXTREMAL HEIGHT

  • MASANOBU KANEKO (a1) and MIKA SAKATA (a2)
Abstract

We give three identities involving multiple zeta values of height one and of maximal height: an explicit formula for the height-one multiple zeta values, a regularised sum formula and a sum formula for the multiple zeta values of maximal height.

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References
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[1]Aomoto, K., ‘Special values of hyperlogarithms and linear difference schemes’, Illinois J. Math. 34(2) (1990), 191216.
[2]Arakawa, T. and Kaneko, M., ‘Multiple zeta values, poly-Bernoulli numbers, and related zeta functions’, Nagoya Math. J. 153 (1999), 189209.
[3]Arakawa, T. and Kaneko, M., ‘On multiple L-values’, J. Math. Soc. Japan 56 (2004), 967991.
[4]Drinfel’d, V. G., ‘On quasitriangular quasi-Hopf algebras and a group closely connected with Gal(ℚ̄∕ℚ)’, Leningrad Math. J. 2 (1991), 829860.
[5]Hoffman, M. E., ‘Multiple harmonic series’, Pacific J. Math. 152 (1992), 275290.
[6]Ihara, K., Kaneko, M. and Zagier, D., ‘Derivation and double shuffle relations for multiple zeta values’, Compositio Math. 142 (2006), 307338.
[7]Kaneko, M. and Tsumura, H., ‘Multi-poly-Bernoulli numbers and related zeta functions’, Preprint, 2015, arXiv:1503.02156.
[8]Ohno, Y. and Zagier, D., ‘Multiple zeta values of fixed weight, depth, and height’, J. Number Theory 74 (1999), 3943.
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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