{"paper":{"title":"A $t$-motivic interpretation of shuffle relations for multizeta values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Wei-Cheng Huang","submitted_at":"2019-04-03T21:48:06Z","abstract_excerpt":"Thakur (2010) showed that, for $r,$ $s\\in \\mathbb{N}$, a product of two Carlitz zeta values $\\zeta_A(r)$ and $\\zeta_A(s)$ can be expressed as an $\\mathbb{F}_p$-linear combination of $\\zeta_A(r+s)$ and double zeta values of weight $r+s$. Such an expression is called shuffle relation by Thakur. Fixing $r,$ $s\\in \\mathbb{N}$, we construct a $t$-module $E'$. To determine whether an $(r+s)$-tuple $\\mathfrak{C}$ in $\\mathbb{F}_q(\\theta)^{r+s}$ gives a shuffle relation, we relate it to the $\\mathbb{F}_q[t]$-torsion property of the point $\\mathbf{v}_\\mathfrak{C}\\in E'(\\mathbb{F}_q[\\theta])$ constructe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02248","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}