Year: 2026
Type: preprint
Abstract: We study the algebra of formal finite multiple zeta values by imposing the stuffle and linear shuffle relations of Kaneko and Zagier. Our first results are a surjective homomorphism to the algebra of formal symmetric multiple zeta values and a parity reduction in depth at most four. In even weight we construct a quotient of the formal double zeta space which is isomorphic to the space of formal finite multiple zeta values of depth at most four. The proof combines an explicit depth-three reduction with a motivic lower bound. We also attach to every even period polynomial an explicit relation among the values $ζ_{A}(2a,1,2b,1)$, and these give all relations among the corresponding formal values.
Source: arXiv (Cornell University)
Authors: Bachmann, Henrik, Risan
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203704451