{"keyword":["Algebra","Number Theory"],"acknowledgement":"This article is a version the author’s master thesis at the University of Bonn. The author would like to thank his advisor Valentin Blomer for introducing the problem, and giving generous feedback and encouragement along the way, especially during the global pandemic.\r\nThe author thanks Edgar Assing for his lectures on analytic number theory. Finally, the author is grateful to the anonymous referees for their valuable time and comments.\r\n","isi":1,"year":"2023","intvolume":"       207","volume":207,"language":[{"iso":"eng"}],"_id":"12406","citation":{"mla":"Diao, Yijie. “Density of the Union of Positive Diagonal Binary Quadratic Forms.” <i>Acta Arithmetica</i>, vol. 207, Instytut Matematyczny, 2023, pp. 1–17, doi:<a href=\"https://doi.org/10.4064/aa210830-24-11\">10.4064/aa210830-24-11</a>.","ieee":"Y. Diao, “Density of the union of positive diagonal binary quadratic forms,” <i>Acta Arithmetica</i>, vol. 207. Instytut Matematyczny, pp. 1–17, 2023.","ama":"Diao Y. Density of the union of positive diagonal binary quadratic forms. <i>Acta Arithmetica</i>. 2023;207:1-17. doi:<a href=\"https://doi.org/10.4064/aa210830-24-11\">10.4064/aa210830-24-11</a>","apa":"Diao, Y. (2023). Density of the union of positive diagonal binary quadratic forms. <i>Acta Arithmetica</i>. Instytut Matematyczny. <a href=\"https://doi.org/10.4064/aa210830-24-11\">https://doi.org/10.4064/aa210830-24-11</a>","chicago":"Diao, Yijie. “Density of the Union of Positive Diagonal Binary Quadratic Forms.” <i>Acta Arithmetica</i>. Instytut Matematyczny, 2023. <a href=\"https://doi.org/10.4064/aa210830-24-11\">https://doi.org/10.4064/aa210830-24-11</a>.","ista":"Diao Y. 2023. Density of the union of positive diagonal binary quadratic forms. Acta Arithmetica. 207, 1–17.","short":"Y. Diao, Acta Arithmetica 207 (2023) 1–17."},"article_type":"original","external_id":{"arxiv":["2103.08268"],"isi":["000912903000001"]},"publication_identifier":{"eissn":["1730-6264"],"issn":["0065-1036"]},"doi":"10.4064/aa210830-24-11","page":"1-17","author":[{"full_name":"Diao, Yijie","id":"7b7eb4ca-eb2c-11ec-b98b-accec0b20c3b","last_name":"Diao","first_name":"Yijie","orcid":"0000-0002-4989-5330"}],"publication":"Acta Arithmetica","quality_controlled":"1","title":"Density of the union of positive diagonal binary quadratic forms","status":"public","publisher":"Instytut Matematyczny","oa":1,"oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2023-01-26T21:17:04Z","department":[{"_id":"GradSch"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2103.08268"}],"abstract":[{"lang":"eng","text":"Let X be a sufficiently large positive integer. We prove that one may choose a subset S of primes with cardinality O(logX) such that a positive proportion of integers less than X can be represented by x2+py2 for at least one p∈S."}],"publication_status":"published","date_published":"2023-01-09T00:00:00Z","article_processing_charge":"No","month":"01","date_updated":"2023-10-17T09:15:17Z","type":"journal_article","day":"09"}