PreprintCC BY 4.0arXiv
Shifted log-sine integrals and multiple zeta values
Abstract
We show that the shifted log-sine integrals with odd entries, introduced by Umezawa, are multiple zeta values. In particular, they define an algebra homomorphism from the f-alphabet algebra to the algebra of multiple zeta values. The proof uses a motivic realization at sixth roots of unity and the Galois descent from level six to level one studied by Glanois. Finally, we give an interpretation of our results using Zinbiel algebras and introduce iterated cotangent integrals.
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BibTeX
@misc{bachmann2026shifted,
title = {{Shifted log-sine integrals and multiple zeta values}},
author = {Henrik Bachmann},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27834},
eprint = {2609.27834},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27834},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Shifted log-sine integrals and multiple zeta values
AU - Henrik Bachmann
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.27834
UR - https://arxiv.org/abs/2609.27834
AB - We show that the shifted log-sine integrals with odd entries, introduced by Umezawa, are multiple zeta values. In particular, they define an algebra homomorphism from the f-alphabet algebra to the algebra of multiple zeta values. The proof uses a motivic realization at sixth roots of unity and the Galois descent from level six to level one studied by Glanois. Finally, we give an interpretation of our results using Zinbiel algebras and introduce iterated cotangent integrals.
ER -