{"paper":{"title":"On the proof of the Prime Number Theorem using Order Estimates for the Chebyshev Theta Function","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.HO","authors_text":"Subham De","submitted_at":"2023-08-14T16:27:47Z","abstract_excerpt":"In this paper, we shall study the stellar work of Norwegian mathematician Selberg and Hungarian mathematician Erd\\H{o}s in providing an Elementary proof of the well-known \\textit{Prime Number Theorem}. In addition to introducing ourselves to the notion of \\textit{Arithmetic Functions}, we shall primarily focus our research on obtaining suitable estimates for the \\textit{Chebyshev Theta Function} $\\vartheta(x)$. Furthermore, we'll try to infer about the asymptotic properties of another function $\\rho(x)$, which shall be needed later on in establishing an equivalent statement of our main result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.07245","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/2308.07245/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"}