发表机构
Graduate School of Mathematics, Nagoya University（名古屋大学大学院理学研究科）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究形式有限多重zeta值的代数，建立其到形式对称多重zeta值代数的满同态、深度不超4的奇偶性归约等成果，构造的商空间可满射对应有限多重zeta值空间，还给出相关显式关系。
AI 中文摘要
我们通过引入Kaneko和Zagier的stuffle与线性shuffle关系，研究形式有限多重zeta值的代数结构。首要成果包括到形式对称多重zeta值代数的满同态，以及深度不超过4的奇偶性归约。在偶权情形下，我们构造形式双zeta空间的一个商空间，该商空间可满射到深度不超过4的有限多重zeta值空间，且对每个偶周期多项式，我们给出了值ζ_A(2a,1,2b,1)之间的显式关系。
英文摘要
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.
Comments35 pages. Update in v2: Former conjecture proved, giving the formal depth-four isomorphism in every even weight
