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