[{"article_processing_charge":"No","day":"15","year":"2021","abstract":[{"text":"We find an asymptotic formula for the number of primitive vectors $(z_1,\\ldots,z_4)\\in (\\mathbb{Z}_{\\neq 0})^4$ such that $z_1,\\ldots, z_4$ are all squareful and bounded by $B$, and $z_1+\\cdots + z_4 = 0$. Our result agrees in the power of $B$ and $\\log B$ with the Campana-Manin conjecture of Pieropan, Smeets, Tanimoto and V\\'{a}rilly-Alvarado.","lang":"eng"}],"_id":"12076","date_created":"2022-09-09T10:42:51Z","doi":"10.48550/arXiv.2104.06966","author":[{"last_name":"Shute","orcid":"0000-0002-1812-2810","full_name":"Shute, Alec L","id":"440EB050-F248-11E8-B48F-1D18A9856A87","first_name":"Alec L"}],"das_tickbox":"0","corr_author":"1","date_published":"2021-04-15T00:00:00Z","supplementarymaterial":"no","oa":1,"status":"public","citation":{"ama":"Shute AL. Sums of four squareful numbers. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2104.06966\">10.48550/arXiv.2104.06966</a>","apa":"Shute, A. L. (n.d.). Sums of four squareful numbers. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2104.06966\">https://doi.org/10.48550/arXiv.2104.06966</a>","short":"A.L. Shute, ArXiv (n.d.).","chicago":"Shute, Alec L. “Sums of Four Squareful Numbers.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2104.06966\">https://doi.org/10.48550/arXiv.2104.06966</a>.","ieee":"A. L. Shute, “Sums of four squareful numbers,” <i>arXiv</i>. .","ista":"Shute AL. Sums of four squareful numbers. arXiv, 2104.06966.","mla":"Shute, Alec L. “Sums of Four Squareful Numbers.” <i>ArXiv</i>, 2104.06966, doi:<a href=\"https://doi.org/10.48550/arXiv.2104.06966\">10.48550/arXiv.2104.06966</a>."},"publication_status":"draft","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2104.06966"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","type":"preprint","arxiv":1,"article_number":"2104.06966","researchdata_availability":"no","external_id":{"arxiv":["2104.06966"]},"title":"Sums of four squareful numbers","date_updated":"2026-08-06T11:08:48Z","department":[{"_id":"TiBr"}],"oa_version":"Preprint","language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"dissertation_contains","id":"12072","status":"public"}]},"publication":"arXiv","month":"04"}]