Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Bachmann, Henrik
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214232761