{"doi":"10.1016/j.jnt.2024.02.013","intvolume":"       261","month":"04","date_updated":"2024-04-29T05:56:34Z","type":"journal_article","date_created":"2024-04-14T22:01:00Z","scopus_import":"1","title":"Square-free values of random polynomials","date_published":"2024-04-02T00:00:00Z","oa":1,"_id":"15312","volume":261,"citation":{"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>.","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>","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>.","short":"T.D. Browning, I.E. Shparlinski, Journal of Number Theory 261 (2024) 220–240.","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>","ista":"Browning TD, Shparlinski IE. 2024. Square-free values of random polynomials. Journal of Number Theory. 261, 220–240."},"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)"},"department":[{"_id":"TiBr"}],"abstract":[{"lang":"eng","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."}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","status":"public","publication_status":"epub_ahead","publication_identifier":{"issn":["0022-314X"]},"article_processing_charge":"No","year":"2024","article_type":"original","external_id":{"arxiv":["2305.15493"]},"page":"220-240","publication":"Journal of Number Theory","language":[{"iso":"eng"}],"author":[{"full_name":"Browning, Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","last_name":"Browning","first_name":"Timothy D"},{"full_name":"Shparlinski, Igor E.","last_name":"Shparlinski","first_name":"Igor E."}],"day":"02","main_file_link":[{"url":"https://doi.org/10.1016/j.jnt.2024.02.013","open_access":"1"}],"oa_version":"Published Version","publisher":"Elsevier"}