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