[{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","arxiv":1,"day":"01","author":[{"full_name":"Bilu, Margaret","id":"98C47862-10D5-11EA-BEDD-0F6F3DDC885E","first_name":"Margaret","last_name":"Bilu"},{"full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D","last_name":"Browning"}],"page":"1179-1242","keyword":["Circle method","moduli spaces of curves","hypersurfaces","Grothendieck ring of varieties","motivic integration"],"article_type":"original","das_tickbox":"0","OA_type":"green","external_id":{"arxiv":["2304.09645"]},"OA_place":"repository","publication":"Annales Scientifiques de l’École Normale Supérieure","date_created":"2026-09-13T22:01:57Z","title":"A motivic circle method","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2304.09645","open_access":"1"}],"issue":"5","month":"05","researchdata_availability":"no","date_updated":"2026-09-17T08:22:39Z","fulldoi":"https://doi.org/10.24033/asens.2628","supplementarymaterial":"yes","language":[{"iso":"eng"}],"department":[{"_id":"TiBr"}],"scopus_import":"1","oa":1,"project":[{"_id":"05A4F6F0-7A3F-11EA-A408-12923DDC885E","name":"A motivic circle method","call_identifier":"H2020","grant_number":"893012"},{"grant_number":"P36278","name":"Rational curves via function field analytic number theory","_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3"}],"article_processing_charge":"No","intvolume":"        58","citation":{"ista":"Bilu M, Browning TD. 2025. A motivic circle method. Annales Scientifiques de l’École Normale Supérieure. 58(5), 1179–1242.","short":"M. Bilu, T.D. Browning, Annales Scientifiques de l’École Normale Supérieure 58 (2025) 1179–1242.","mla":"Bilu, Margaret, and Timothy D. Browning. “A Motivic Circle Method.” <i>Annales Scientifiques de l’École Normale Supérieure</i>, vol. 58, no. 5, Société Mathématique de France, 2025, pp. 1179–242, doi:<a href=\"https://doi.org/10.24033/asens.2628\">10.24033/asens.2628</a>.","ieee":"M. Bilu and T. D. Browning, “A motivic circle method,” <i>Annales Scientifiques de l’École Normale Supérieure</i>, vol. 58, no. 5. Société Mathématique de France, pp. 1179–1242, 2025.","chicago":"Bilu, Margaret, and Timothy D Browning. “A Motivic Circle Method.” <i>Annales Scientifiques de l’École Normale Supérieure</i>. Société Mathématique de France, 2025. <a href=\"https://doi.org/10.24033/asens.2628\">https://doi.org/10.24033/asens.2628</a>.","apa":"Bilu, M., &#38; Browning, T. D. (2025). A motivic circle method. <i>Annales Scientifiques de l’École Normale Supérieure</i>. Société Mathématique de France. <a href=\"https://doi.org/10.24033/asens.2628\">https://doi.org/10.24033/asens.2628</a>","ama":"Bilu M, Browning TD. A motivic circle method. <i>Annales Scientifiques de l’École Normale Supérieure</i>. 2025;58(5):1179-1242. doi:<a href=\"https://doi.org/10.24033/asens.2628\">10.24033/asens.2628</a>"},"publication_identifier":{"issn":["0012-9593"],"eissn":["1873-2151"]},"publisher":"Société Mathématique de France","ec_funded":1,"publication_status":"published","abstract":[{"lang":"eng","text":"The circle method has been successfully used over the last century to study rational points on hypersurfaces. More recently, a version of the method over function fields, combined with spreading out techniques, has led to a range of results about moduli spaces of rational curves on hypersurfaces. In this paper a version of the circle method is implemented in the setting of the Grothendieck ring of varieties. This allows us to approximate the classes of these moduli spaces directly, without relying on point counting, and leads to a deeper understanding of their geometry."},{"lang":"fre","text":"La méthode du cercle a été utilisée avec succès au cours du siècle dernier pour l’étude\r\ndes points rationnels sur les hypersurfaces. Plus récemment, une version fonctionnelle de cette méthode,\r\ncombinée à des techniques d’étalement, a mené à une série de résultats sur les espaces de modules de\r\ncourbes sur les hypersurfaces. Dans cet article on implémente une version de la méthode du cercle dans\r\nle cadre de l’anneau de Grothendieck des variétés. Cela permet d’approximer les classes de ces espaces\r\nde modules directement, sans recours au comptage de points, ce qui donne accès à une compréhension\r\nplus profonde de leur géométrie."}],"corr_author":"1","oa_version":"Preprint","acknowledgement":"The authors are grateful to Yohan Brunebarbe, Tom Burel, Antoine\r\nChambert-Loir, Loïs Faisant, Mirko Mauri and Will Sawin for useful comments. Thanks are\r\nalso due to the anonymous referees for numerous helpful remarks. M.B. received funding\r\nfrom the European Union’s Horizon 2020 research and innovation programme under the\r\nMarie Skłodowska-Curie Grant agreement No. 893012. T.B. was supported by a FWF grant\r\n(DOI 10.55776/P36278) and by a grant from the Institute for Advanced Study School of\r\nMathematics.","doi":"10.24033/asens.2628","quality_controlled":"1","volume":58,"year":"2025","status":"public","date_published":"2025-05-01T00:00:00Z","_id":"22929"}]