{"citation":{"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>","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>.","ieee":"A. L. Shute, “Sums of four squareful numbers,” <i>arXiv</i>. .","ista":"Shute AL. Sums of four squareful numbers. arXiv, 2104.06966.","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>","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>.","short":"A.L. Shute, ArXiv (n.d.)."},"month":"04","external_id":{"arxiv":["2104.06966"]},"oa":1,"author":[{"full_name":"Shute, Alec L","id":"440EB050-F248-11E8-B48F-1D18A9856A87","last_name":"Shute","first_name":"Alec L","orcid":"0000-0002-1812-2810"}],"abstract":[{"lang":"eng","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."}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","related_material":{"record":[{"relation":"dissertation_contains","id":"12072","status":"public"}]},"article_number":"2104.06966","date_created":"2022-09-09T10:42:51Z","oa_version":"Preprint","date_published":"2021-04-15T00:00:00Z","title":"Sums of four squareful numbers","article_processing_charge":"No","type":"preprint","publication":"arXiv","doi":"10.48550/arXiv.2104.06966","department":[{"_id":"TiBr"}],"publication_status":"submitted","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2104.06966","open_access":"1"}],"language":[{"iso":"eng"}],"_id":"12076","year":"2021","date_updated":"2023-02-21T16:37:30Z","day":"15","status":"public"}