[{"oa":1,"_id":"12308","title":"Primitive divisors of sequences associated to elliptic curves with complex multiplication","publication":"Research in Number Theory","publication_status":"published","abstract":[{"text":"Let P and Q be two points on an elliptic curve defined over a number field K. For α∈End(E), define Bα to be the OK-integral ideal generated by the denominator of x(α(P)+Q). Let O be a subring of End(E), that is a Dedekind domain. We will study the sequence {Bα}α∈O. We will show that, for all but finitely many α∈O, the ideal Bα has a primitive divisor when P is a non-torsion point and there exist two endomorphisms g≠0 and f so that f(P)=g(Q). This is a generalization of previous results on elliptic divisibility sequences.","lang":"eng"}],"quality_controlled":"1","extern":"1","author":[{"id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","full_name":"Verzobio, Matteo","orcid":"0000-0002-0854-0306","first_name":"Matteo","last_name":"Verzobio"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s40993-021-00267-9"}],"citation":{"apa":"Verzobio, M. (2021). Primitive divisors of sequences associated to elliptic curves with complex multiplication. <i>Research in Number Theory</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s40993-021-00267-9\">https://doi.org/10.1007/s40993-021-00267-9</a>","mla":"Verzobio, Matteo. “Primitive Divisors of Sequences Associated to Elliptic Curves with Complex Multiplication.” <i>Research in Number Theory</i>, vol. 7, no. 2, 37, Springer Nature, 2021, doi:<a href=\"https://doi.org/10.1007/s40993-021-00267-9\">10.1007/s40993-021-00267-9</a>.","ieee":"M. Verzobio, “Primitive divisors of sequences associated to elliptic curves with complex multiplication,” <i>Research in Number Theory</i>, vol. 7, no. 2. Springer Nature, 2021.","ama":"Verzobio M. Primitive divisors of sequences associated to elliptic curves with complex multiplication. <i>Research in Number Theory</i>. 2021;7(2). doi:<a href=\"https://doi.org/10.1007/s40993-021-00267-9\">10.1007/s40993-021-00267-9</a>","chicago":"Verzobio, Matteo. “Primitive Divisors of Sequences Associated to Elliptic Curves with Complex Multiplication.” <i>Research in Number Theory</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s40993-021-00267-9\">https://doi.org/10.1007/s40993-021-00267-9</a>.","short":"M. Verzobio, Research in Number Theory 7 (2021).","ista":"Verzobio M. 2021. Primitive divisors of sequences associated to elliptic curves with complex multiplication. Research in Number Theory. 7(2), 37."},"year":"2021","intvolume":"         7","article_number":"37","status":"public","date_created":"2023-01-16T11:44:39Z","month":"05","volume":7,"issue":"2","publisher":"Springer Nature","article_type":"original","doi":"10.1007/s40993-021-00267-9","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","day":"20","type":"journal_article","date_updated":"2023-05-08T12:00:17Z","oa_version":"Published Version","publication_identifier":{"issn":["2522-0160","2363-9555"]},"scopus_import":"1","date_published":"2021-05-20T00:00:00Z","keyword":["Algebra and Number Theory"]}]