English

Some Remarks on Maesaka-Seki-Watanabe's Formula for the Multiple Harmonic Sums

Number Theory 2025-04-11 v2

Abstract

Recently, Maesaka, Seki and Watanabe discovered a surprising equality between multiple harmonic sums and certain Riemann sums which approximate the iterated integral expression of the multiple zeta values. In this paper, we describe the formula corresponding to the multiple zeta-star values and, more generally, to the Schur multiple zeta values of diagonally constant indices. We also discuss the relationship of these formulas with Hoffman's duality identity and an identity due to Kawashima.

Keywords

Cite

@article{arxiv.2403.03498,
  title  = {Some Remarks on Maesaka-Seki-Watanabe's Formula for the Multiple Harmonic Sums},
  author = {Shuji Yamamoto},
  journal= {arXiv preprint arXiv:2403.03498},
  year   = {2025}
}

Comments

14 pages; some errors and unnatural expressions are corrected; to be published in the Journal of the Mathematical Society of Japan