[{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Noam","last_name":"Kimmel","full_name":"Kimmel, Noam"},{"id":"c3bac823-112d-11f0-a3f5-c264f852e697","full_name":"Kuperberg, Vivian Zieve","first_name":"Vivian Zieve","last_name":"Kuperberg"}],"extern":"1","OA_place":"repository","volume":24,"title":"Positive density for consecutive runs of sums of two squares","article_processing_charge":"No","page":"1995-2046","publication_status":"published","external_id":{"arxiv":["2406.04174"]},"abstract":[{"lang":"eng","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"}],"publication_identifier":{"issn":["1474-7480"],"eissn":["1475-3030"]},"doi":"10.1017/s1474748025000131","issue":"5","publication":"Journal of the Institute of Mathematics of Jussieu","date_created":"2026-06-29T13:01:08Z","year":"2025","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2406.04174","open_access":"1"}],"quality_controlled":"1","scopus_import":"1","_id":"22204","oa_version":"Preprint","intvolume":"        24","article_type":"original","type":"journal_article","date_published":"2025-09-01T00:00:00Z","language":[{"iso":"eng"}],"month":"09","date_updated":"2026-07-14T11:50:36Z","publisher":"Cambridge University Press","arxiv":1,"oa":1,"status":"public","day":"01","OA_type":"green","citation":{"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>","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.","short":"N. Kimmel, V.Z. Kuperberg, Journal of the Institute of Mathematics of Jussieu 24 (2025) 1995–2046.","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>.","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>.","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>"}},{"date_updated":"2026-07-29T09:57:08Z","department":[{"_id":"TiBr"}],"arxiv":1,"publisher":"Cambridge University Press","date_published":"2024-11-01T00:00:00Z","language":[{"iso":"eng"}],"month":"11","file_date_updated":"2025-01-09T08:56:33Z","oa":1,"isi":1,"scopus_import":"1","_id":"15338","acknowledgement":"The authors are grateful to Jayce Getz for asking questions that set this project in motion and to the anonymous referee for useful comments. T.B. was supported by a FWF grant (DOI 10.55776/P32428) and by a grant from the Institute for Advanced Study School of Mathematics. L.B.P. was partially supported by NSF DMS-2200470 and DMS-1652173, and thanks the Hausdorff Centre for Mathematics for hosting research visits.","type":"journal_article","oa_version":"Published Version","intvolume":"        23","article_type":"original","project":[{"grant_number":"P32428","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","name":"New frontiers of the Manin conjecture","call_identifier":"FWF"}],"citation":{"mla":"Browning, Timothy D., et al. “Generalised Quadratic Forms over Totally Real Number Fields.” <i>Journal of the Institute of Mathematics of Jussieu</i>, vol. 23, no. 6, Cambridge University Press, 2024, pp. 2859–912, doi:<a href=\"https://doi.org/10.1017/S1474748024000161\">10.1017/S1474748024000161</a>.","chicago":"Browning, Timothy D, Lillian B. Pierce, and Damaris Schindler. “Generalised Quadratic Forms over Totally Real Number Fields.” <i>Journal of the Institute of Mathematics of Jussieu</i>. Cambridge University Press, 2024. <a href=\"https://doi.org/10.1017/S1474748024000161\">https://doi.org/10.1017/S1474748024000161</a>.","apa":"Browning, T. D., Pierce, L. B., &#38; Schindler, D. (2024). Generalised quadratic forms over totally real number fields. <i>Journal of the Institute of Mathematics of Jussieu</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/S1474748024000161\">https://doi.org/10.1017/S1474748024000161</a>","ista":"Browning TD, Pierce LB, Schindler D. 2024. Generalised quadratic forms over totally real number fields. Journal of the Institute of Mathematics of Jussieu. 23(6), 2859–2912.","ama":"Browning TD, Pierce LB, Schindler D. Generalised quadratic forms over totally real number fields. <i>Journal of the Institute of Mathematics of Jussieu</i>. 2024;23(6):2859-2912. doi:<a href=\"https://doi.org/10.1017/S1474748024000161\">10.1017/S1474748024000161</a>","ieee":"T. D. Browning, L. B. Pierce, and D. Schindler, “Generalised quadratic forms over totally real number fields,” <i>Journal of the Institute of Mathematics of Jussieu</i>, vol. 23, no. 6. Cambridge University Press, pp. 2859–2912, 2024.","short":"T.D. Browning, L.B. Pierce, D. Schindler, Journal of the Institute of Mathematics of Jussieu 23 (2024) 2859–2912."},"status":"public","day":"01","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"OA_type":"hybrid","title":"Generalised quadratic forms over totally real number fields","external_id":{"isi":["001200337400001"],"arxiv":["2212.11038"]},"publication_status":"published","abstract":[{"lang":"eng","text":"We introduce a new class of generalised quadratic forms over totally real number fields, which is rich enough to capture the arithmetic of arbitrary systems of quadrics over the rational numbers. We explore this connection through a version of the Hardy–Littlewood circle method over number fields."}],"article_processing_charge":"Yes (via OA deal)","page":"2859-2912","volume":23,"OA_place":"publisher","author":[{"full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87","last_name":"Browning","first_name":"Timothy D"},{"full_name":"Pierce, Lillian B.","first_name":"Lillian B.","last_name":"Pierce"},{"first_name":"Damaris","last_name":"Schindler","full_name":"Schindler, Damaris"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","ddc":["510"],"has_accepted_license":"1","file":[{"file_id":"18793","date_updated":"2025-01-09T08:56:33Z","file_size":690974,"checksum":"b300541d581a71d92314df5ae8c4cc09","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_name":"2024_JournInstMathJussieu_Browning.pdf","date_created":"2025-01-09T08:56:33Z","creator":"dernst","success":1}],"quality_controlled":"1","supplementarymaterial":"no","corr_author":"1","das_tickbox":"0","publication":"Journal of the Institute of Mathematics of Jussieu","doi":"10.1017/S1474748024000161","publication_identifier":{"eissn":["1475-3030"],"issn":["1474-7480"]},"issue":"6","researchdata_availability":"no","date_created":"2024-04-21T22:00:53Z","year":"2024"}]