{"paper":{"title":"Prime Number Theorems for Polynomials from Homogeneous Dynamics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Giorgos Kotsovolis, Katharine Woo","submitted_at":"2023-12-18T18:49:50Z","abstract_excerpt":"We establish a new class of examples of the multivariate Bateman-Horn conjecture by using tools from dynamics. These cases include the determinant polynomial on the space of $n\\times n$ matrices, the Pfaffian on the space of skew-symmetric $2n\\times 2n$ matrices, and the determinant polynomial on the space of symmetric $n\\times n$ matrices. In particular, let $(V,F)$ be any pair among the following: $(\\textrm{Mat}_n, \\det)$, $(\\textrm{Skew}_{2n},\\textrm{Pff})$, and $(\\textrm{Sym}_n, \\det).$ We then obtain an asymptotic for $$\\pi_{V,F}(T)= \\#\\{v\\in V: \\max(|v_i|)\\leq T, F(v) \\text{ is prime}\\},"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.11445","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.11445/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}