Article Dans Une Revue Journal of Number Theory Année : 2024

Generalisations of multiple zeta values to rooted forests

Résumé

We show that any convergent (shuffle) arborified zeta value admits a series representation. This justifies the introduction of a new generalisation to rooted forests of multiple zeta values, and we study its algebraic properties. As a consequence of the series representation, we derive elementary proofs of some results of Bradley and Zhou for Mordell-Tornheim zeta values and give explicit formulas. The series representation for shuffle arborified zeta values also implies that they are conical zeta values. We characterise which conical zeta values are arborified zeta values and evaluate them as sums of multiple zeta values with rational coefficients.

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Dates et versions

hal-04940850 , version 1 (13-03-2025)
hal-04940850 , version 2 (12-05-2025)

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Pierre J. Clavier, Dorian Perrot. Generalisations of multiple zeta values to rooted forests. Journal of Number Theory, 2024, 264, pp.233-276. ⟨10.1016/j.jnt.2024.05.008⟩. ⟨hal-04940850v2⟩
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