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- Title
Trivial multiple zeta values in Tate algebras.
- Authors
Gezmiş, O; Pellarin, F
- Abstract
We study trivial multiple zeta values in Tate algebras. These are particular examples of the multiple zeta values in Tate algebras introduced by the second author. If the number of variables involved is "not large" in a way that is made precise in the paper, we can endow the set of trivial multiple zeta values with a structure of module over a non-commutative polynomial ring with coefficients in the rational fraction field over |${\mathbb{F}}_q$|. We determine the structure of this module in terms of generators and we show how in many cases, this is sufficient for the detection of linear relations between Thakur's multiple zeta values.
- Subjects
NONCOMMUTATIVE rings; ALGEBRA; ZETA functions; POLYNOMIAL rings
- Publication
IMRN: International Mathematics Research Notices, 2022, Vol 2022, Issue 18, p14319
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnab104