[{"abstract":[{"lang":"eng","text":"The large sieve is used to estimate the density of quadratic polynomials Q ∈ Z[x],\r\nsuch that there exists an odd degree polynomial defined over Z which has resultant ±1 with Q.\r\nGiven a monic polynomial R ∈ Z[x] of odd degree, this is used to show that for almost all\r\nquadratic polynomials Q ∈ Z[x], there exists a prime p such that Q and R share a common\r\nroot in Fp. Using recent work of Landesman, an application to the average size of the odd part\r\nof the class group of quadratic number fields is also given"},{"lang":"fre","text":" Le grand crible est utilisé pour estimer la densité des polynômes quadratiques Q ∈ Z[x] tels qu’il existe un polynôme de degré impair défini sur Z dont le résultant avec Q est égal à ±1. Étant donné un polynôme unitaire R ∈ Z[x] de degré impair, on s’en sert pour montrer que, pour presque tous les polynômes quadratiques Q ∈ Z[x], il existe un nombre premier p tel que Q et R aient une racine commune dans Fp. En utilisant des travaux récents de Landesman, on obtient également une application concernant la taille moyenne de la partie impaire du groupe de classe des corps quadratiques."}],"file_date_updated":"2026-02-24T07:56:34Z","oa_version":"Published Version","language":[{"iso":"eng"}],"page":"1677-1691","article_processing_charge":"Yes","article_type":"original","quality_controlled":"1","intvolume":"        12","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"volume":12,"type":"journal_article","status":"public","scopus_import":"1","department":[{"_id":"TiBr"}],"acknowledgement":"While working on this paper, the first author was supported by a FWF grant (DOI 10.55776/P36278).","DOAJ_listed":"1","date_published":"2025-10-21T00:00:00Z","arxiv":1,"has_accepted_license":"1","OA_place":"publisher","project":[{"_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3","name":"Rational curves via function field analytic number theory","grant_number":"P36278"}],"oa":1,"date_created":"2026-02-22T23:01:36Z","ddc":["510"],"day":"21","_id":"21343","OA_type":"gold","publication_status":"published","file":[{"date_updated":"2026-02-24T07:56:34Z","file_id":"21356","file_name":"2025_JEP_Browning.pdf","success":1,"checksum":"828577ea48ac6109d3e9dd1aeddd45c4","creator":"dernst","content_type":"application/pdf","access_level":"open_access","date_created":"2026-02-24T07:56:34Z","relation":"main_file","file_size":1003689}],"month":"10","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.5802/jep.320","author":[{"last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D","first_name":"Timothy D","orcid":"0000-0002-8314-0177"},{"first_name":"Yik Tung","orcid":"0000-0001-8467-4106","full_name":"Chan, Yik Tung","id":"c4c0afc8-9262-11ed-9231-d8b0bc743af1","last_name":"Chan"}],"external_id":{"arxiv":["2411.09264"]},"citation":{"ama":"Browning TD, Chan S. Solubility of a resultant equation and applications. <i>Journal de l’ecole polytechnique mathematiques</i>. 2025;12:1677-1691. doi:<a href=\"https://doi.org/10.5802/jep.320\">10.5802/jep.320</a>","chicago":"Browning, Timothy D, and Stephanie Chan. “Solubility of a Resultant Equation and Applications.” <i>Journal de l’ecole Polytechnique Mathematiques</i>. Ecole polytechnique, 2025. <a href=\"https://doi.org/10.5802/jep.320\">https://doi.org/10.5802/jep.320</a>.","ista":"Browning TD, Chan S. 2025. Solubility of a resultant equation and applications. Journal de l’ecole polytechnique mathematiques. 12, 1677–1691.","apa":"Browning, T. D., &#38; Chan, S. (2025). Solubility of a resultant equation and applications. <i>Journal de l’ecole Polytechnique Mathematiques</i>. Ecole polytechnique. <a href=\"https://doi.org/10.5802/jep.320\">https://doi.org/10.5802/jep.320</a>","short":"T.D. Browning, S. Chan, Journal de l’ecole Polytechnique Mathematiques 12 (2025) 1677–1691.","mla":"Browning, Timothy D., and Stephanie Chan. “Solubility of a Resultant Equation and Applications.” <i>Journal de l’ecole Polytechnique Mathematiques</i>, vol. 12, Ecole polytechnique, 2025, pp. 1677–91, doi:<a href=\"https://doi.org/10.5802/jep.320\">10.5802/jep.320</a>.","ieee":"T. D. Browning and S. Chan, “Solubility of a resultant equation and applications,” <i>Journal de l’ecole polytechnique mathematiques</i>, vol. 12. Ecole polytechnique, pp. 1677–1691, 2025."},"PlanS_conform":"1","title":"Solubility of a resultant equation and applications","publication_identifier":{"issn":["2429-7100"],"eissn":["2270-518X"]},"year":"2025","corr_author":"1","date_updated":"2026-02-24T07:57:53Z","publisher":"Ecole polytechnique","publication":"Journal de l'ecole polytechnique mathematiques"},{"isi":1,"department":[{"_id":"JaMa"}],"scopus_import":"1","has_accepted_license":"1","date_published":"2024-01-01T00:00:00Z","arxiv":1,"oa_version":"Published Version","language":[{"iso":"eng"}],"page":"957-1010","file_date_updated":"2024-10-01T07:31:56Z","abstract":[{"text":"We study the geometry of Poisson point processes from the point of view of optimal transport and Ricci lower bounds. We construct a Riemannian structure on the space of point processes and the associated distance W that corresponds to the Benamou–Brenier variational formula. Our main tool is a non-local continuity equation formulated with the difference operator. The closure of the domain of the relative entropy is a complete geodesic space, when endowed with \r\nW. The geometry of this non-local infinite-dimensional space is analogous to that of spaces with positive Ricci curvature. Among others: (a) the Ornstein–Uhlenbeck semi-group is the gradient flow of the relative entropy; (b) the Poisson space has an entropic Ricci curvature bounded from below by 1; (c) W satisfies an HWI inequality.","lang":"eng"},{"text":"Nous étudions la géométrie des processus ponctuels de Poisson à travers le prisme du transport optimal et de la minoration de la courbure de Ricci. Nous construisons une structure\r\nriemannienne sur l’espace des processus ponctuels et la distance associée W qui concorde avec la formulation variationnelle de Benamou–Brenier. Notre analyse repose sur une équation de continuité non locale définie à l’aide de l’opérateur de différence. La fermeture du domaine de l’entropie relative, équipé de W, est un espace géodésique complet. La géométrie de cet espace non local et de dimension infinie est analogue à celle des espaces à courbure de Ricci strictement positive. Entre autres : (a) le semi-groupe d’Ornstein–Uhlenbeck est le flot du gradient de l’entropie relative ; (b) l’espace de Poisson a une courbure de Ricci entropique minorée par 1 ; (c) W satisfait une inégalité HWI.","lang":"fre"}],"article_type":"original","quality_controlled":"1","article_processing_charge":"Yes","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"intvolume":"        11","volume":11,"status":"public","type":"journal_article","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","month":"01","author":[{"first_name":"Lorenzo","orcid":"0000-0002-9881-6870","full_name":"Dello Schiavo, Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","last_name":"Dello Schiavo"},{"first_name":"Ronan","last_name":"Herry","full_name":"Herry, Ronan"},{"first_name":"Kohei","full_name":"Suzuki, Kohei","last_name":"Suzuki"}],"doi":"10.5802/jep.270","external_id":{"isi":["001367254000003"],"arxiv":["2303.00398"]},"citation":{"ista":"Dello Schiavo L, Herry R, Suzuki K. 2024. Wasserstein geometry and Ricci curvature bounds for Poisson spaces. Journal de l’Ecole Polytechnique - Mathematiques. 11, 957–1010.","chicago":"Dello Schiavo, Lorenzo, Ronan Herry, and Kohei Suzuki. “Wasserstein Geometry and Ricci Curvature Bounds for Poisson Spaces.” <i>Journal de l’Ecole Polytechnique - Mathematiques</i>. Ecole Polytechnique, 2024. <a href=\"https://doi.org/10.5802/jep.270\">https://doi.org/10.5802/jep.270</a>.","ama":"Dello Schiavo L, Herry R, Suzuki K. Wasserstein geometry and Ricci curvature bounds for Poisson spaces. <i>Journal de l’Ecole Polytechnique - Mathematiques</i>. 2024;11:957-1010. doi:<a href=\"https://doi.org/10.5802/jep.270\">10.5802/jep.270</a>","ieee":"L. Dello Schiavo, R. Herry, and K. Suzuki, “Wasserstein geometry and Ricci curvature bounds for Poisson spaces,” <i>Journal de l’Ecole Polytechnique - Mathematiques</i>, vol. 11. Ecole Polytechnique, pp. 957–1010, 2024.","mla":"Dello Schiavo, Lorenzo, et al. “Wasserstein Geometry and Ricci Curvature Bounds for Poisson Spaces.” <i>Journal de l’Ecole Polytechnique - Mathematiques</i>, vol. 11, Ecole Polytechnique, 2024, pp. 957–1010, doi:<a href=\"https://doi.org/10.5802/jep.270\">10.5802/jep.270</a>.","short":"L. Dello Schiavo, R. Herry, K. Suzuki, Journal de l’Ecole Polytechnique - Mathematiques 11 (2024) 957–1010.","apa":"Dello Schiavo, L., Herry, R., &#38; Suzuki, K. (2024). Wasserstein geometry and Ricci curvature bounds for Poisson spaces. <i>Journal de l’Ecole Polytechnique - Mathematiques</i>. Ecole Polytechnique. <a href=\"https://doi.org/10.5802/jep.270\">https://doi.org/10.5802/jep.270</a>"},"title":"Wasserstein geometry and Ricci curvature bounds for Poisson spaces","publication_identifier":{"eissn":["2270-518X"],"issn":["2429-7100"]},"publication":"Journal de l'Ecole Polytechnique - Mathematiques","corr_author":"1","year":"2024","date_updated":"2025-09-08T09:50:50Z","publisher":"Ecole Polytechnique","date_created":"2024-09-29T22:01:38Z","ddc":["510"],"oa":1,"day":"01","_id":"18158","file":[{"content_type":"application/pdf","creator":"dernst","checksum":"5a51da5fb5f7fcaada378d43444cced8","relation":"main_file","file_size":1250553,"access_level":"open_access","date_created":"2024-10-01T07:31:56Z","file_name":"2024_JourEcolePolytechniqueMath_DelloSchiavo.pdf","file_id":"18164","success":1,"date_updated":"2024-10-01T07:31:56Z"}],"publication_status":"published"},{"oa":1,"date_created":"2018-12-11T11:45:03Z","ddc":["510"],"day":"01","_id":"180","ec_funded":1,"publication_status":"published","file":[{"relation":"main_file","file_size":843938,"access_level":"open_access","date_created":"2018-12-17T16:38:18Z","checksum":"1ba7cccdf3900f42c4f715ae75d6813c","content_type":"application/pdf","creator":"dernst","file_id":"5726","file_name":"2018_JournaldeLecoleMath_Lewi.pdf","date_updated":"2020-07-14T12:45:16Z"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"07","publist_id":"7741","author":[{"last_name":"Lewi","full_name":"Lewi, Mathieu","first_name":"Mathieu"},{"first_name":"Élliott","full_name":"Lieb, Élliott","last_name":"Lieb"},{"last_name":"Seiringer","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","first_name":"Robert"}],"doi":"10.5802/jep.64","citation":{"ama":"Lewi M, Lieb É, Seiringer R. Statistical mechanics of the uniform electron gas. <i>Journal de l’Ecole Polytechnique - Mathematiques</i>. 2018;5:79-116. doi:<a href=\"https://doi.org/10.5802/jep.64\">10.5802/jep.64</a>","chicago":"Lewi, Mathieu, Élliott Lieb, and Robert Seiringer. “Statistical Mechanics of the Uniform Electron Gas.” <i>Journal de l’Ecole Polytechnique - Mathematiques</i>. Ecole Polytechnique, 2018. <a href=\"https://doi.org/10.5802/jep.64\">https://doi.org/10.5802/jep.64</a>.","ista":"Lewi M, Lieb É, Seiringer R. 2018. Statistical mechanics of the uniform electron gas. Journal de l’Ecole Polytechnique - Mathematiques. 5, 79–116.","short":"M. Lewi, É. Lieb, R. Seiringer, Journal de l’Ecole Polytechnique - Mathematiques 5 (2018) 79–116.","apa":"Lewi, M., Lieb, É., &#38; Seiringer, R. (2018). Statistical mechanics of the uniform electron gas. <i>Journal de l’Ecole Polytechnique - Mathematiques</i>. Ecole Polytechnique. <a href=\"https://doi.org/10.5802/jep.64\">https://doi.org/10.5802/jep.64</a>","mla":"Lewi, Mathieu, et al. “Statistical Mechanics of the Uniform Electron Gas.” <i>Journal de l’Ecole Polytechnique - Mathematiques</i>, vol. 5, Ecole Polytechnique, 2018, pp. 79–116, doi:<a href=\"https://doi.org/10.5802/jep.64\">10.5802/jep.64</a>.","ieee":"M. Lewi, É. Lieb, and R. Seiringer, “Statistical mechanics of the uniform electron gas,” <i>Journal de l’Ecole Polytechnique - Mathematiques</i>, vol. 5. Ecole Polytechnique, pp. 79–116, 2018."},"external_id":{"arxiv":["1705.10676"]},"title":"Statistical mechanics of the uniform electron gas","publication_identifier":{"eissn":["2270-518X"],"issn":["2429-7100"]},"year":"2018","publisher":"Ecole Polytechnique","date_updated":"2025-04-14T07:26:59Z","publication":"Journal de l'Ecole Polytechnique - Mathematiques","file_date_updated":"2020-07-14T12:45:16Z","abstract":[{"text":"In this paper we define and study the classical Uniform Electron Gas (UEG), a system of infinitely many electrons whose density is constant everywhere in space. The UEG is defined differently from Jellium, which has a positive constant background but no constraint on the density. We prove that the UEG arises in Density Functional Theory in the limit of a slowly varying density, minimizing the indirect Coulomb energy. We also construct the quantum UEG and compare it to the classical UEG at low density.","lang":"eng"}],"oa_version":"Published Version","license":"https://creativecommons.org/licenses/by-nd/4.0/","page":"79 - 116","language":[{"iso":"eng"}],"article_processing_charge":"No","article_type":"original","quality_controlled":"1","tmp":{"name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","image":"/image/cc_by_nd.png","short":"CC BY-ND (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode"},"intvolume":"         5","volume":5,"type":"journal_article","status":"public","scopus_import":"1","department":[{"_id":"RoSe"}],"acknowledgement":"This project has received funding from the European Research Council (ERC) under the European\r\nUnion’s Horizon 2020 research and innovation programme (grant agreement 694227 for R.S. and MDFT 725528 for M.L.). Financial support by the Austrian Science Fund (FWF), project No P 27533-N27 (R.S.) and by the US National Science Foundation, grant No PHY12-1265118 (E.H.L.) are gratefully acknowledged.","date_published":"2018-07-01T00:00:00Z","arxiv":1,"has_accepted_license":"1","project":[{"grant_number":"694227","name":"Analysis of quantum many-body systems","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"},{"name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","grant_number":"P27533_N27","_id":"25C878CE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}]}]