{"paper":{"title":"On the Invariants of Towers of Function Fields over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Florian Hess, Henning Stichtenoth, Seher Tutdere","submitted_at":"2011-11-23T19:54:58Z","abstract_excerpt":"We consider a tower of function fields F=(F_n)_{n\\geq 0} over a finite field F_q and a finite extension E/F_0 such that the sequence \\mathcal{E):=(EF_n)_{n\\goq 0} is a tower over the field F_q. Then we deal with the following: What can we say about the invariants of \\mathcal{E}; i.e., the asymptotic number of places of degree r for any r\\geq 1 in \\mathcal{E}, if those of F are known? We give a method based on explicit extensions for constructing towers of function fields over F_q with finitely many prescribed invariants being positive, and towers of function fields over F_q, for q a square, wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5600","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"}