Weighted sum formula for multiple harmonic sums modulo primes
Minoru Hirose, Hideki Murahara, Shingo Saito
TL;DR
This paper proves a weighted sum formula for multiple harmonic sums modulo primes, extending to finite multiple zeta values, using difference equations, and proposes related conjectures.
Contribution
It introduces a new weighted sum formula for multiple harmonic sums modulo primes and finite multiple zeta values, with a novel proof technique.
Findings
Proved a weighted sum formula for multiple harmonic sums modulo primes
Extended the formula to finite multiple zeta values
Proposed conjectures for similar weighted sum formulas
Abstract
In this paper we prove a weighted sum formula for multiple harmonic sums modulo primes, thereby proving a weighted sum formula for finite multiple zeta values. Our proof utilizes difference equations for the generating series of multiple harmonic sums. We also conjecture several weighted sum formulas of similar flavor for finite multiple zeta values.
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Taxonomy
TopicsAdvanced Mathematical Identities · Analytic Number Theory Research · Advanced Combinatorial Mathematics