Work

A determinant formula for multiple harmonic sums and their linear independence

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.27767

Authors: Hirose, Minoru, Murahara, Hideki, Saito, Shingo

Institution: Kagoshima University

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

OpenAlex ID: W7223143391

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