An interpolation of Ohno's relation to complex functions

  • Minoru Hirose
  • Hideki Murahara
  • Tomokazu Onozuka

Abstract

Ohno's relation is a well known formula among multiple zeta values. In this paper, we present its interpolation to complex functions.

References

Akiyama, S., Egami, S., and Tanigawa, Y., Analytic continuation of multiple zeta-functions and their values at non-positive integers, Acta Arith. 98 (2001), no. 2, 107–116. https://doi.org/10.4064/aa98-2-1

Apostol, T. M., Introduction to analytic number theory, Undergraduate Texts in Mathematics, Springer-Verlag, New York-Heidelberg, 1976.

Hirose, M., Murahara, H., and Onozuka, T., Sum formula for multiple zeta function, eprint arXiv:1808.01559 [math.NT], 2018.

Ikeda, S. and Matsuoka, K., On the functional relations for the Euler-Zagier multiple zeta-functions, Tokyo J. Math. 41 (2018), no. 2, 477–485.

Komori, Y., Matsumoto, K., and Tsumura, H., On Witten multiple zeta-functions associated with semisimple Lie algebras II, J. Math. Soc. Japan 62 (2010), no. 2, 355–394.

Matsumoto, K., On the analytic continuation of various multiple zeta-functions, in “Number theory for the millennium, II (Urbana, IL, 2000)”, A K Peters, Natick, MA, 2002, pp. 417–440.

Matsumoto, K., Analytic properties of multiple zeta-functions in several variables, in “Number theory”, Dev. Math., vol. 15, Springer, New York, 2006, pp. 153–173. https://doi.org/10.1007/0-387-30829-6_11

Matsumoto, K. and Tsumura, H., Functional relations for various multiple zeta-functions, in “Analytic Number Theory (Kyoto, 2005)”, RIMS Kôkyûroku, no. 1512, 2006, pp. 179–190.

Matsumoto, K. and Tsumura, H., On Witten multiple zeta-functions associated with semisimple Lie algebras. I, Ann. Inst. Fourier (Grenoble) 56 (2006), no. 5, 1457–1504.

Nakamura, T., A functional relation for the Tornheim double zeta function, Acta Arith. 125 (2006), no. 3, 257–263. https://doi.org/10.4064/aa125-3-3

Ohno, Y., A generalization of the duality and sum formulas on the multiple zeta values, J. Number Theory 74 (1999), no. 1, 39–43. https://doi.org/10.1006/jnth.1998.2314

Tsumura, H., On functional relations between the Mordell-Tornheim double zeta functions and the Riemann zeta function, Math. Proc. Cambridge Philos. Soc. 142 (2007), no. 3, 395–405. https://doi.org/10.1017/S0305004107000059

Zhao, J., Analytic continuation of multiple zeta functions, Proc. Amer. Math. Soc. 128 (2000), no. 5, 1275–1283. https://doi.org/10.1090/S0002-9939-99-05398-8

Zhao, J. and Zhou, X., Witten multiple zeta values attached to $\mathfrak sl(4)$, Tokyo J. Math. 34 (2011), no. 1, 135–152. https://doi.org/10.3836/tjm/1313074447
Published
2020-05-06
How to Cite
Hirose, M., Murahara, H., & Onozuka, T. (2020). An interpolation of Ohno’s relation to complex functions. MATHEMATICA SCANDINAVICA, 126(2), 293-297. https://doi.org/10.7146/math.scand.a-119209
Section
Articles