{"paper":{"title":"Some new congruences on biregular overpartitions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"N. K. Meher","submitted_at":"2025-07-02T09:35:01Z","abstract_excerpt":"Recently, Nadji, Ahmia and Ram\\'{i}rez \\cite{Nadji2025} investigate the arithmetic properties of ${\\bar B}_{\\ell_1,\\ell_2}(n)$, the number of overpartitions where no part is divisible by $\\ell_1$ or $\\ell_2$ with $\\gcd(\\ell_1,\\ell_2)$$=1$ and $\\ell_1$,$\\ell_2$$>1$. Specifically, they established congruences modulo $3$ and powers of $2$ for the pairs of $(\\ell_1,\\ell_2)$$\\in$$\\{(4,3),(4,9),(8,3),(8,9)\\}$, using the concept of generating functions, dissection formulas and Smoot's implementation of Radu's Ramanujan-Kolberg algorithm. After that, Alanazi, Munagi and Saikia \\cite{Alanazi2024} studi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.01529","kind":"arxiv","version":2},"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/2507.01529/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"}