PreprintarXiv licencearXiv
A determinant formula for multiple harmonic sums and their linear independence
Abstract
We explicitly evaluate a family of determinants whose entries are multiple harmonic sums. As a consequence, we prove that certain finite sequences of multiple harmonic sums are linearly independent. This result strengthens the previously known linear independence of the corresponding infinite sequences and stands in contrast to the abundance of linear relations among multiple zeta values.
Related
- The threshold for linear independence of multiple zeta values in positive characteristic
- Improved Upper Bounds for the Rank of the Determinant Tensor via Glynn's Formula
- Combinatorics of noncommutative harmonic oscillator determinant
- An Almgren-type formula for planar p-harmonic functions
- Linear maps preserving the Cullis' determinant. III
BibTeX
@misc{hirose2026determinant,
title = {{A determinant formula for multiple harmonic sums and their linear independence}},
author = {Minoru Hirose and Hideki Murahara and Shingo Saito},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27767},
eprint = {2610.27767},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27767},
}
RIS
TY - UNPB
TI - A determinant formula for multiple harmonic sums and their linear independence
AU - Minoru Hirose
AU - Hideki Murahara
AU - Shingo Saito
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27767
UR - https://arxiv.org/abs/2610.27767
AB - We explicitly evaluate a family of determinants whose entries are multiple harmonic sums. As a consequence, we prove that certain finite sequences of multiple harmonic sums are linearly independent. This result strengthens the previously known linear independence of the corresponding infinite sequences and stands in contrast to the abundance of linear relations among multiple zeta values.
ER -