[{"external_id":{"arxiv":["2510.26191"]},"publisher":"Oxford University Press","month":"10","department":[{"_id":"TiBr"}],"day":"06","oa":1,"corr_author":"1","doi":"10.1093/qmath/haag037","researchdata_availability":"no","article_number":"haag037","publication_status":"epub_ahead","quality_controlled":"1","year":"2026","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"ddc":["500"],"das_tickbox":"0","fulldoi":"https://doi.org/10.1093/qmath/haag037","main_file_link":[{"url":"https://doi.org/10.1093/qmath/haag037","open_access":"1"}],"arxiv":1,"has_accepted_license":"1","date_published":"2026-10-06T00:00:00Z","article_processing_charge":"Yes (via OA deal)","publication_identifier":{"eissn":["1464-3847"],"issn":["0033-5606"]},"acknowledgement":"The authors are very grateful to Pierre Le Boudec, whose contributions would have merited coauthorship. At his request, however, he is not listed as a co-author, since he has chosen to pursue\r\na career outside academia. T.B. was supported by a grant from the IAS School of Mathematics\r\nand a FWF grant (DOI 10.55776/P36278). W.S. was supported by NSF grant DMS-2502029 and\r\na Sloan Research Fellowship.","publication":"The Quarterly Journal of Mathematics","scopus_import":"1","language":[{"iso":"eng"}],"OA_place":"publisher","OA_type":"hybrid","type":"journal_article","oa_version":"Published Version","article_type":"original","abstract":[{"lang":"eng","text":"Among the set of hypersurfaces of degree d and dimension  defined by the vanishing\r\nof a homogeneous polynomial with coefficients in the set {−1, +1}, we investigate the\r\nprobability that a hypersurface contains a rational point as d and  tend to ∞."}],"title":"Random diophantine equations of large degree","_id":"23124","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":"Sawin, Will","first_name":"Will","last_name":"Sawin"}],"date_created":"2026-10-12T13:58:16Z","status":"public","supplementarymaterial":"no","date_updated":"2026-10-14T08:49:05Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","PlanS_conform":"1","citation":{"chicago":"Browning, Timothy D, and Will Sawin. “Random Diophantine Equations of Large Degree.” <i>The Quarterly Journal of Mathematics</i>. Oxford University Press, 2026. <a href=\"https://doi.org/10.1093/qmath/haag037\">https://doi.org/10.1093/qmath/haag037</a>.","apa":"Browning, T. D., &#38; Sawin, W. (2026). Random diophantine equations of large degree. <i>The Quarterly Journal of Mathematics</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/qmath/haag037\">https://doi.org/10.1093/qmath/haag037</a>","ama":"Browning TD, Sawin W. Random diophantine equations of large degree. <i>The Quarterly Journal of Mathematics</i>. 2026. doi:<a href=\"https://doi.org/10.1093/qmath/haag037\">10.1093/qmath/haag037</a>","mla":"Browning, Timothy D., and Will Sawin. “Random Diophantine Equations of Large Degree.” <i>The Quarterly Journal of Mathematics</i>, haag037, Oxford University Press, 2026, doi:<a href=\"https://doi.org/10.1093/qmath/haag037\">10.1093/qmath/haag037</a>.","short":"T.D. Browning, W. Sawin, The Quarterly Journal of Mathematics (2026).","ieee":"T. D. Browning and W. Sawin, “Random diophantine equations of large degree,” <i>The Quarterly Journal of Mathematics</i>. Oxford University Press, 2026.","ista":"Browning TD, Sawin W. 2026. Random diophantine equations of large degree. The Quarterly Journal of Mathematics., haag037."},"project":[{"grant_number":"P36278","name":"Rational curves via function field analytic number theory","_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3"}]}]