[{"external_id":{"arxiv":["2103.08268"],"isi":["000912903000001"]},"isi":1,"citation":{"ista":"Diao Y. 2023. Density of the union of positive diagonal binary quadratic forms. Acta Arithmetica. 207, 1–17.","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>.","short":"Y. Diao, Acta Arithmetica 207 (2023) 1–17.","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>.","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.","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>","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>"},"year":"2023","date_updated":"2023-10-17T09:15:17Z","abstract":[{"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.","lang":"eng"}],"day":"09","arxiv":1,"doi":"10.4064/aa210830-24-11","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","volume":207,"author":[{"id":"7b7eb4ca-eb2c-11ec-b98b-accec0b20c3b","orcid":"0000-0002-4989-5330","full_name":"Diao, Yijie","first_name":"Yijie","last_name":"Diao"}],"_id":"12406","intvolume":"       207","title":"Density of the union of positive diagonal binary quadratic forms","article_processing_charge":"No","department":[{"_id":"GradSch"}],"date_created":"2023-01-26T21:17:04Z","publication_status":"published","quality_controlled":"1","page":"1-17","article_type":"original","publisher":"Instytut Matematyczny","type":"journal_article","date_published":"2023-01-09T00:00:00Z","oa":1,"publication_identifier":{"eissn":["1730-6264"],"issn":["0065-1036"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2103.08268","open_access":"1"}],"publication":"Acta Arithmetica","month":"01","oa_version":"Preprint","keyword":["Algebra","Number Theory"],"language":[{"iso":"eng"}]},{"article_type":"original","publisher":"Institute of Mathematics, Polish Academy of Sciences","page":"129-168","quality_controlled":"1","title":"Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728","intvolume":"       198","publication_status":"published","article_processing_charge":"No","date_created":"2023-01-16T11:44:54Z","author":[{"id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","orcid":"0000-0002-0854-0306","full_name":"Verzobio, Matteo","first_name":"Matteo","last_name":"Verzobio"}],"issue":"2","_id":"12309","scopus_import":"1","extern":"1","volume":198,"abstract":[{"text":"Take a rational elliptic curve defined by the equation y2=x3+ax in minimal form and consider the sequence Bn of the denominators of the abscissas of the iterate of a non-torsion point. We show that B5m has a primitive divisor for every m. Then, we show how to generalize this method to the terms of the form Bmp with p a prime congruent to 1 modulo 4.","lang":"eng"}],"doi":"10.4064/aa191016-30-7","arxiv":1,"day":"04","external_id":{"arxiv":["2001.09634"]},"date_updated":"2023-05-08T11:58:14Z","year":"2021","citation":{"ama":"Verzobio M. Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728. <i>Acta Arithmetica</i>. 2021;198(2):129-168. doi:<a href=\"https://doi.org/10.4064/aa191016-30-7\">10.4064/aa191016-30-7</a>","apa":"Verzobio, M. (2021). Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728. <i>Acta Arithmetica</i>. Institute of Mathematics, Polish Academy of Sciences. <a href=\"https://doi.org/10.4064/aa191016-30-7\">https://doi.org/10.4064/aa191016-30-7</a>","chicago":"Verzobio, Matteo. “Primitive Divisors of Elliptic Divisibility Sequences for Elliptic Curves with J=1728.” <i>Acta Arithmetica</i>. Institute of Mathematics, Polish Academy of Sciences, 2021. <a href=\"https://doi.org/10.4064/aa191016-30-7\">https://doi.org/10.4064/aa191016-30-7</a>.","ieee":"M. Verzobio, “Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728,” <i>Acta Arithmetica</i>, vol. 198, no. 2. Institute of Mathematics, Polish Academy of Sciences, pp. 129–168, 2021.","mla":"Verzobio, Matteo. “Primitive Divisors of Elliptic Divisibility Sequences for Elliptic Curves with J=1728.” <i>Acta Arithmetica</i>, vol. 198, no. 2, Institute of Mathematics, Polish Academy of Sciences, 2021, pp. 129–68, doi:<a href=\"https://doi.org/10.4064/aa191016-30-7\">10.4064/aa191016-30-7</a>.","short":"M. Verzobio, Acta Arithmetica 198 (2021) 129–168.","ista":"Verzobio M. 2021. Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728. Acta Arithmetica. 198(2), 129–168."},"language":[{"iso":"eng"}],"keyword":["Algebra and Number Theory"],"month":"01","oa_version":"Preprint","publication":"Acta Arithmetica","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2001.09634"}],"oa":1,"publication_identifier":{"issn":["0065-1036","1730-6264"]},"date_published":"2021-01-04T00:00:00Z","type":"journal_article"}]