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Rooted tree maps for multiple $L$-values from a perspective of harmonic algebras

Hideki Murahara, Tatsushi Tanaka and Noriko Wakabayashi
Vol. 18 (2024), No. 11, 2003–2025
DOI: 10.2140/ant.2024.18.2003
Abstract

We show the image of rooted tree maps forms a subspace of the kernel of the evaluation map of multiple L-values. To prove this, we define the diamond product as a modified harmonic product and describe its properties. We also show that τ-conjugate rooted tree maps are their antipodes.

Keywords
Connes–Kreimer Hopf algebra of rooted trees, rooted tree maps, harmonic products, multiple zeta values, multiple $L$-values
Mathematical Subject Classification
Primary: 11M32
Secondary: 05C05, 16T05
Milestones
Received: 30 October 2022
Revised: 8 October 2023
Accepted: 27 November 2023
Published: 18 October 2024
Authors
Hideki Murahara
Department of Mathematics
The University of Kitakyushu
Fukuoka
Japan
Tatsushi Tanaka
Department of Mathematics
Kyoto Sangyo University
Kyoto
Japan
Noriko Wakabayashi
Center of Physics and Mathematics
Osaka Electro-Communication University
Osaka
Japan
© 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY).

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