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ON A GENERALISATION OF A RESTRICTED SUM FORMULA FOR MULTIPLE ZETA VALUES AND FINITE MULTIPLE ZETA VALUES

  • HIDEKI MURAHARA (a1) and TAKUYA MURAKAMI (a2)

Abstract

We prove a new linear relation for multiple zeta values. This is a natural generalisation of the restricted sum formula proved by Eie, Liaw and Ong. We also present an analogous result for finite multiple zeta values.

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[1] Eie, M., Liaw, W.-C. and Ong, Y. L., ‘A restricted sum formula among multiple zeta values’, J. Number Theory 129 (2009), 908921.
[2] Horikawa, Y., Oyama, K. and Murahara, H., ‘A note on derivation relations for multiple zeta values and finite multiple zeta values’, Preprint, 2018, arXiv:1809.08389[NT].
[3] Ihara, K., Kaneko, M. and Zagier, D., ‘Derivation and double shuffle relations for multiple zeta values’, Compos. Math. 142 (2006), 307338.
[4] Kaneko, M., ‘Finite multiple zeta values’, RIMS Kôkyûroku Bessatsu B68 (2017), 175190 (in Japanese).
[5] Kaneko, M. and Yamamoto, S., ‘A new integral-series identity of multiple zeta values and regularizations’, Selecta Math. (N.S.) 24 (2018), 24992521.
[6] Kaneko, M. and Zagier, D., ‘Finite multiple zeta values’, in preparation.
[7] Murahara, H., ‘Derivation relations for finite multiple zeta values’, Int. J. Number 13 (2017), 419427.
[8] Oyama, K., ‘Ohno-type relation for finite multiple zeta values’, Kyushu J. Math. 72 (2018), 277285.
[9] Tanaka, T., ‘Restricted sum formula and derivation relation for multiple zeta values’, Preprint, 2013, arXiv:1303.0398 [NT].
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ON A GENERALISATION OF A RESTRICTED SUM FORMULA FOR MULTIPLE ZETA VALUES AND FINITE MULTIPLE ZETA VALUES

  • HIDEKI MURAHARA (a1) and TAKUYA MURAKAMI (a2)

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