{"paper":{"title":"A Point Counting Algorithm for Cyclic Covers of the Projective Line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","math.NT"],"primary_cat":"cs.CG","authors_text":"C\\'ecile Gon\\c{c}alves (INRIA Saclay - Ile de France, LIX)","submitted_at":"2014-08-09T13:26:36Z","abstract_excerpt":"We present a Kedlaya-style point counting algorithm for cyclic covers $y^r = f(x)$ over a finite field $\\mathbb{F}_{p^n}$ with $p$ not dividing $r$, and $r$ and $\\deg{f}$ not necessarily coprime. This algorithm generalizes the Gaudry-G\\\"urel algorithm for superelliptic curves to a more general class of curves, and has essentially the same complexity. Our practical improvements include a simplified algorithm exploiting the automorphism of $\\mathcal{C}$, refined bounds on the $p$-adic precision, and an alternative pseudo-basis for the Monsky-Washnitzer cohomology which leads to an integral matri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2095","kind":"arxiv","version":2},"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"}