[{"intvolume":"        24","publication_status":"published","type":"journal_article","publisher":"Cambridge University Press","citation":{"apa":"Kimmel, N., &#38; Kuperberg, V. Z. (2025). Positive density for consecutive runs of sums of two squares. <i>Journal of the Institute of Mathematics of Jussieu</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/s1474748025000131\">https://doi.org/10.1017/s1474748025000131</a>","mla":"Kimmel, Noam, and Vivian Zieve Kuperberg. “Positive Density for Consecutive Runs of Sums of Two Squares.” <i>Journal of the Institute of Mathematics of Jussieu</i>, vol. 24, no. 5, Cambridge University Press, 2025, pp. 1995–2046, doi:<a href=\"https://doi.org/10.1017/s1474748025000131\">10.1017/s1474748025000131</a>.","ista":"Kimmel N, Kuperberg VZ. 2025. Positive density for consecutive runs of sums of two squares. Journal of the Institute of Mathematics of Jussieu. 24(5), 1995–2046.","ieee":"N. Kimmel and V. Z. Kuperberg, “Positive density for consecutive runs of sums of two squares,” <i>Journal of the Institute of Mathematics of Jussieu</i>, vol. 24, no. 5. Cambridge University Press, pp. 1995–2046, 2025.","chicago":"Kimmel, Noam, and Vivian Zieve Kuperberg. “Positive Density for Consecutive Runs of Sums of Two Squares.” <i>Journal of the Institute of Mathematics of Jussieu</i>. Cambridge University Press, 2025. <a href=\"https://doi.org/10.1017/s1474748025000131\">https://doi.org/10.1017/s1474748025000131</a>.","short":"N. Kimmel, V.Z. Kuperberg, Journal of the Institute of Mathematics of Jussieu 24 (2025) 1995–2046.","ama":"Kimmel N, Kuperberg VZ. Positive density for consecutive runs of sums of two squares. <i>Journal of the Institute of Mathematics of Jussieu</i>. 2025;24(5):1995-2046. doi:<a href=\"https://doi.org/10.1017/s1474748025000131\">10.1017/s1474748025000131</a>"},"abstract":[{"text":"We study the distribution of consecutive sums of two squares in arithmetic progressions. We\r\nshow that for any odd squarefree modulus q, any two reduced congruence classes a1 and a2 mod q,\r\nand any r1,r2 ≥ 1, a positive density of sums of two squares begin a chain of r1 consecutive sums of\r\ntwo squares, all of which are a1 mod q, followed immediately by a chain of r2 consecutive sums of two\r\nsquares, all of which are a2 mod q. This is an analog of the result of Maynard for the sequence of primes,\r\nshowing that for any reduced congruence class a mod q and for any r ≥ 1, a positive density of primes\r\nbegin a sequence of r consecutive primes, all of which are a mod q","lang":"eng"}],"scopus_import":"1","doi":"10.1017/s1474748025000131","month":"09","issue":"5","page":"1995-2046","article_processing_charge":"No","language":[{"iso":"eng"}],"volume":24,"quality_controlled":"1","year":"2025","publication":"Journal of the Institute of Mathematics of Jussieu","extern":"1","oa_version":"Preprint","date_created":"2026-06-29T13:01:08Z","_id":"22204","external_id":{"arxiv":["2406.04174"]},"oa":1,"date_published":"2025-09-01T00:00:00Z","OA_type":"green","publication_identifier":{"eissn":["1475-3030"],"issn":["1474-7480"]},"arxiv":1,"OA_place":"repository","article_type":"original","day":"01","author":[{"last_name":"Kimmel","first_name":"Noam","full_name":"Kimmel, Noam"},{"full_name":"Kuperberg, Vivian Zieve","first_name":"Vivian Zieve","last_name":"Kuperberg","id":"c3bac823-112d-11f0-a3f5-c264f852e697"}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2406.04174","open_access":"1"}],"title":"Positive density for consecutive runs of sums of two squares","status":"public","date_updated":"2026-07-14T11:50:36Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"}]