{"abstract":[{"text":"The question of whether or not a given integral polynomial takes infinitely many square-free values has only been addressed unconditionally for polynomials of degree at most 3. We address this question, on average, for polynomials of arbitrary degree.","lang":"eng"}],"year":"2024","publication_identifier":{"issn":["0022-314X"]},"publisher":"Elsevier","article_type":"original","status":"public","oa_version":"Published Version","department":[{"_id":"TiBr"}],"citation":{"ista":"Browning TD, Shparlinski IE. 2024. Square-free values of random polynomials. Journal of Number Theory. 261, 220–240.","short":"T.D. Browning, I.E. Shparlinski, Journal of Number Theory 261 (2024) 220–240.","ama":"Browning TD, Shparlinski IE. Square-free values of random polynomials. <i>Journal of Number Theory</i>. 2024;261:220-240. doi:<a href=\"https://doi.org/10.1016/j.jnt.2024.02.013\">10.1016/j.jnt.2024.02.013</a>","ieee":"T. D. Browning and I. E. Shparlinski, “Square-free values of random polynomials,” <i>Journal of Number Theory</i>, vol. 261. Elsevier, pp. 220–240, 2024.","mla":"Browning, Timothy D., and Igor E. Shparlinski. “Square-Free Values of Random Polynomials.” <i>Journal of Number Theory</i>, vol. 261, Elsevier, 2024, pp. 220–40, doi:<a href=\"https://doi.org/10.1016/j.jnt.2024.02.013\">10.1016/j.jnt.2024.02.013</a>.","chicago":"Browning, Timothy D, and Igor E. Shparlinski. “Square-Free Values of Random Polynomials.” <i>Journal of Number Theory</i>. Elsevier, 2024. <a href=\"https://doi.org/10.1016/j.jnt.2024.02.013\">https://doi.org/10.1016/j.jnt.2024.02.013</a>.","apa":"Browning, T. D., &#38; Shparlinski, I. E. (2024). Square-free values of random polynomials. <i>Journal of Number Theory</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jnt.2024.02.013\">https://doi.org/10.1016/j.jnt.2024.02.013</a>"},"type":"journal_article","date_created":"2024-04-14T22:01:00Z","article_processing_charge":"No","scopus_import":"1","month":"04","date_updated":"2024-04-29T05:56:34Z","title":"Square-free values of random polynomials","oa":1,"tmp":{"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)","image":"/images/cc_by.png"},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1016/j.jnt.2024.02.013"}],"intvolume":"       261","language":[{"iso":"eng"}],"quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"220-240","date_published":"2024-04-02T00:00:00Z","publication_status":"epub_ahead","day":"02","publication":"Journal of Number Theory","external_id":{"arxiv":["2305.15493"]},"author":[{"full_name":"Browning, Timothy D","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","first_name":"Timothy D"},{"first_name":"Igor E.","last_name":"Shparlinski","full_name":"Shparlinski, Igor E."}],"doi":"10.1016/j.jnt.2024.02.013","_id":"15312","volume":261}