{"paper":{"title":"Linear equations in Piatetski-Shapiro primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Xuancheng Shao, Yu-Chen Sun","submitted_at":"2026-05-18T17:15:41Z","abstract_excerpt":"We establish discorrelation estimates between the Piatetski-Shapiro prime set \\[ \\mathcal{P}_{\\gamma} := \\{p \\text{ is prime and } p = \\lfloor n^{1/\\gamma} \\rfloor \\text{ for some } n \\in \\mathbb{N}\\} \\] and arbitrary nilsequences when $\\gamma \\in (0,1)$ is sufficiently close to $1$. This extends earlier works which treated linear or polynomial exponential phase functions. As an application, we establish an asymptotic formula for the number of solutions in $\\mathcal{P}_{\\gamma}$ to any \"finite-complexity\" system of linear equations, including for the number of $k$-term arithmetic progressions "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18676","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/2605.18676/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T00:01:59.125496Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"ed7118ea759ec249048326a34a4efec5bad12f00a09c50b518f4fb8303579051"},"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"}