{"external_id":{"arxiv":["1910.05207"]},"date_created":"2024-04-03T08:12:59Z","doi":"10.2140/ant.2021.15.2195","publication_identifier":{"eissn":["1944-7833"],"issn":["1937-0652"]},"keyword":["Algebra and Number Theory"],"department":[{"_id":"TiBr"}],"status":"public","day":"23","date_updated":"2024-04-09T08:45:26Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1910.05207"}],"intvolume":"        15","citation":{"ieee":"M. Bilu and S. Howe, “Motivic Euler products in motivic statistics,” <i>Algebra &#38; Number Theory</i>, vol. 15, no. 9. Mathematical Sciences Publishers, pp. 2195–2259, 2021.","ista":"Bilu M, Howe S. 2021. Motivic Euler products in motivic statistics. Algebra &#38; Number Theory. 15(9), 2195–2259.","mla":"Bilu, Margaret, and Sean Howe. “Motivic Euler Products in Motivic Statistics.” <i>Algebra &#38; Number Theory</i>, vol. 15, no. 9, Mathematical Sciences Publishers, 2021, pp. 2195–259, doi:<a href=\"https://doi.org/10.2140/ant.2021.15.2195\">10.2140/ant.2021.15.2195</a>.","apa":"Bilu, M., &#38; Howe, S. (2021). Motivic Euler products in motivic statistics. <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/ant.2021.15.2195\">https://doi.org/10.2140/ant.2021.15.2195</a>","ama":"Bilu M, Howe S. Motivic Euler products in motivic statistics. <i>Algebra &#38; Number Theory</i>. 2021;15(9):2195-2259. doi:<a href=\"https://doi.org/10.2140/ant.2021.15.2195\">10.2140/ant.2021.15.2195</a>","short":"M. Bilu, S. Howe, Algebra &#38; Number Theory 15 (2021) 2195–2259.","chicago":"Bilu, Margaret, and Sean Howe. “Motivic Euler Products in Motivic Statistics.” <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers, 2021. <a href=\"https://doi.org/10.2140/ant.2021.15.2195\">https://doi.org/10.2140/ant.2021.15.2195</a>."},"article_processing_charge":"No","oa_version":"Preprint","publication_status":"published","language":[{"iso":"eng"}],"type":"journal_article","month":"12","publisher":"Mathematical Sciences Publishers","date_published":"2021-12-23T00:00:00Z","quality_controlled":"1","article_type":"original","issue":"9","publication":"Algebra & Number Theory","author":[{"last_name":"Bilu","id":"98C47862-10D5-11EA-BEDD-0F6F3DDC885E","first_name":"Margaret","full_name":"Bilu, Margaret"},{"first_name":"Sean","full_name":"Howe, Sean","last_name":"Howe"}],"abstract":[{"lang":"eng","text":"We formulate and prove an analog of Poonen’s finite-field Bertini theorem with Taylor conditions that holds in the Grothendieck ring of varieties. This gives a broad generalization of the work of Vakil and Wood, who treated the case of smooth hypersurface sections, and is made possible by the use of motivic Euler products to write down candidate motivic probabilities. As applications, we give motivic analogs of many results in arithmetic statistics that have been proven using Poonen’s sieve, including work of Bucur and Kedlaya on complete intersections and Erman and Wood on semiample Bertini theorems."}],"page":"2195-2259","oa":1,"volume":15,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"15279","title":"Motivic Euler products in motivic statistics","year":"2021"}