{"paper":{"title":"A hybrid of two theorems of Piatetski-Shapiro","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Angel Kumchev, Zhivko Petrov","submitted_at":"2018-03-11T12:15:02Z","abstract_excerpt":"Let $c > 1$ and $0 < \\gamma < 1$ be real, with $c \\notin \\mathbb N$. We study the solubility of the Diophantine inequality \\[ \\left| p_1^c + p_2^c + \\dots + p_s^c - N \\right| < \\varepsilon \\] in Piatetski-Shapiro primes $p_1, p_2, \\dots, p_s$ of index $\\gamma$---that is, primes of the form $p = \\lfloor m^{1/\\gamma} \\rfloor$ for some $m \\in \\mathbb N$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03952","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"}