{"title":"Sums of four squareful numbers","arxiv":1,"date_published":"2021-04-15T00:00:00Z","article_processing_charge":"No","month":"04","external_id":{"arxiv":["2104.06966"]},"date_updated":"2026-08-06T11:08:48Z","das_tickbox":"0","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2104.06966"}],"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>","ieee":"A. L. Shute, “Sums of four squareful numbers,” <i>arXiv</i>. .","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>.","short":"A.L. Shute, ArXiv (n.d.).","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>."},"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_number":"2104.06966","oa_version":"Preprint","type":"preprint","status":"public","related_material":{"record":[{"id":"12072","relation":"dissertation_contains","status":"public"}]},"supplementarymaterial":"no","date_created":"2022-09-09T10:42:51Z","year":"2021","oa":1,"publication_status":"draft","doi":"10.48550/arXiv.2104.06966","language":[{"iso":"eng"}],"author":[{"orcid":"0000-0002-1812-2810","first_name":"Alec L","last_name":"Shute","full_name":"Shute, Alec L","id":"440EB050-F248-11E8-B48F-1D18A9856A87"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","_id":"12076","department":[{"_id":"TiBr"}],"corr_author":"1","publication":"arXiv","day":"15","researchdata_availability":"no"}