{"paper":{"title":"On subfields of the second generalization of the GK maximal function field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Maria Montanucci, Peter Beelen","submitted_at":"2018-10-31T18:22:54Z","abstract_excerpt":"The second generalized GK function fields $K_n$ are a recently found family of maximal function fields over the finite field with $q^{2n}$ elements, where $q$ is a prime power and $n \\ge 1$ an odd integer. In this paper we construct many new maximal function fields by determining various Galois subfields of $K_n$. In case $\\gcd(q+1,n)=1$ and either $q$ is even or $q \\equiv 1 \\pmod{4},$ we find a complete list of Galois subfields of $K_n.$ Our construction adds several previously unknown genera to the genus spectrum of maximal curves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.00049","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"}