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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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[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.
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[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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