The proof finds multiple zeta values can be expressed as linear combinations of harmonic sums, suggesting a new algorithm for representation.
We prove that every multiple zeta value is a Z-linear combination of ζ(k₁,, kᵣ) where kᵢ≥ 2. Our proof also yields an explicit algorithm for such an expansion. The key ingredient is to introduce modified multiple harmonic sums that partially satisfy the relations among multiple zeta values and to determine the structure of the space generated by them.
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Hirose et al. (2025) studied this question.
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