{"paper":{"title":"A Hilbert-Kunz function with a periodic term that has a given period","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Robin Baidya","submitted_at":"2019-06-20T19:48:17Z","abstract_excerpt":"A result of Monsky states that the Hilbert-Kunz function of a one-dimensional local ring of prime characteristic has a term $\\phi$ that is eventually periodic. For example, in the case of a power series ring in one variable over a prime-characteristic field, $\\phi$ is the zero function and is therefore immediately periodic with period 1. In additional examples produced by Kunz and Monsky, $\\phi$ is immediately periodic with period 2. We show that, for every positive integer $\\pi$, there exists a ring for which $\\phi$ is immediately periodic with period $\\pi$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.08821","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"}