{"paper":{"title":"Fast Coefficient Computation for Algebraic Power Series in Positive Characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"math.NT","authors_text":"Alin Bostan (SPECFUN), Gilles Christol (IMJ), Philippe Dumas (SPECFUN), Xavier Caruso (LAGA)","submitted_at":"2018-06-18T08:18:04Z","abstract_excerpt":"We revisit Christol's theorem on algebraic power series in positive characteristic and propose yet another proof for it. This new proof combines several ingredients and advantages of existing proofs, which make it very well-suited for algorithmic purposes. We apply the construction used in the new proof to the design of a new efficient algorithm for computing the $N$th coefficient of a given algebraic power series over a perfect field of characteristic~$p$. It has several nice features: it is more general, more natural and more efficient than previous algorithms. Not only the arithmetic comple"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06543","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"}