Cyclotomic analogues of finite multiple zeta values

Abstract

We introduce the notion of finite multiple harmonic q-series at a primitive root of unity and show that these specialize to the finite multiple zeta value (FMZV) and the symmetrized multiple zeta value (SMZV) through an algebraic and analytic operation, respectively. Further, we obtain families of linear relations among these series which induce linear relations among FMZVs and SMZVs of the same form. This gives evidence towards a conjecture of Kaneko and Zagier relating FMZVs and SMZVs. Motivated by the above results, we define cyclotomic analogues of FMZVs, which conjecturally generate a vector space of the same dimension as that spanned by the finite multiple harmonic q-series at a primitive root of unity of sufficiently large degree.

23 pages

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• Duality for Finite Multiple Harmonic q-Series
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Cited by in corpus (5)

• Yamamoto's interpolation of finite multiple zeta and zeta-star values
• Derivations on the algebra of multiple harmonic q-series and their applications
• The method of creative microscoping
• Finite and symmetric Mordell-Tornheim multiple zeta values
• Sum of interpolated finite multiple harmonic $q$-series