Multiple zeta values and their q-analogues

2020/07/17 by Abel Vleeshouwers, Vleeshouwers, Abel
Mathematics · #11M32 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2007.08865

openalex publication_date 2020/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We explore the theory of multiple zeta values (MZVs) and some of their q-generalisations. Multiple zeta values are numerical quantities that satisfy several combinatorial relations over the rationals. These relations include two multiplicative relations, which arise naturally from comparison of the MZVs with an underlying algebraic structure. We generalise these concepts by introducing the parameter q in such a way that as q→ 1^- we return to the ordinary MZVs. Our special interest lies in two q-models recently introduced by H. Bachmann. He further conjectures that the ℚ-spaces generated by these q-generalisations coincide. In this thesis we establish a particular case of Bachmann's conjecture.

Related

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