{"paper":{"title":"New uniform and asymptotic upper bounds on the tensor rank of multiplication in extensions of finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hugues Randriam, Julia Pieltant","submitted_at":"2013-05-22T15:21:29Z","abstract_excerpt":"We obtain new uniform upper bounds for the (non necessarily symmetric) tensor rank of the multiplication in the extensions of the finite fields $\\F_q$ for any prime or prime power $q\\geq2$; moreover these uniform bounds lead to new asymptotic bounds as well. In addition, we also give purely asymptotic bounds which are substantially better by using a family of Shimura curves defined over $\\F_q$, with an optimal ratio of $\\F_{q^t}$-rational places to their genus where $q^t$ is a square."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5166","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"}