{"paper":{"title":"Popular differences in primes along fractional powers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bora \\c{C}al{\\i}m, Deborah Wooton, Ioannis Iakovakis, Jack Moffatt, Sophie Long","submitted_at":"2024-11-26T17:06:47Z","abstract_excerpt":"We prove that $\\mathop{\\mathbb{E}}_{m \\leq M} \\mathop{\\mathbb{E}}_{n \\leq N} \\Lambda(n) \\Lambda\\bigl(n + \\lfloor m^c \\rfloor\\bigr) = 1 + \\rm{O}(\\log^{2 - Bc} N)$, where $c > 2$ is a non-integer, $B \\geq 3/c$, and $M$ is of order $N^{1/c} \\log^{-B} N$. As a combinatorial consequence, we obtain that the primes contain infinitely many pairs whose difference belongs to the Piatetski-Shapiro sequence $\\bigl\\{\\lfloor m^c \\rfloor \\colon m \\in \\mathbb{N} \\bigr\\}$ for any non-integer $c > 2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.17599","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/2411.17599/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"}