| _version_ | 1866901812173340672 |
|---|---|
| author | Yang, G.M. |
| author_facet | Yang, G.M. |
| contents | <p>Our first contribution is a unified derivation of generating functions for $\zeta(\{s\}_n)$, $\zeta(\{\bar{s}\}_n)$, and $\lambda(\{s\}_n)$, obtained through Newton-type recursion formulas that refine classical symmetric-function identities. We further establish a closed combinatorial expression for the expansion coefficients of $\lambda(\{2p\}_n)$, which highlights the structural role of root-of-unity symmetries. Finally, for $\lambda(\{3\}_n)$ we prove that no such representation exists in the commutative setting, thereby motivating a non-commutative framework. Within this framework, the commutation condition $[m(x),m(-x)]=0$ leads naturally to the notion of pairwise centrality, while the sum-zero and full 2-step nilpotent constraints subsequently emerge as higher-order structural requirements ensuring global commutativity.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17764766 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Repeated-Index Multiple Zeta Values and Dirichlet Lambda Analogues Yang, G.M. <p>Our first contribution is a unified derivation of generating functions for $\zeta(\{s\}_n)$, $\zeta(\{\bar{s}\}_n)$, and $\lambda(\{s\}_n)$, obtained through Newton-type recursion formulas that refine classical symmetric-function identities. We further establish a closed combinatorial expression for the expansion coefficients of $\lambda(\{2p\}_n)$, which highlights the structural role of root-of-unity symmetries. Finally, for $\lambda(\{3\}_n)$ we prove that no such representation exists in the commutative setting, thereby motivating a non-commutative framework. Within this framework, the commutation condition $[m(x),m(-x)]=0$ leads naturally to the notion of pairwise centrality, while the sum-zero and full 2-step nilpotent constraints subsequently emerge as higher-order structural requirements ensuring global commutativity.</p> |
| title | Repeated-Index Multiple Zeta Values and Dirichlet Lambda Analogues |
| url | https://doi.org/10.5281/zenodo.17764766 |