[{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version","title":"Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve","isi":1,"external_id":{"isi":["001541172400002"],"arxiv":["2309.09699"]},"department":[{"_id":"TiBr"}],"ddc":["500"],"file":[{"success":1,"date_created":"2026-07-23T11:32:51Z","checksum":"34e6e965a2b30a258e0d4103350a68fd","file_name":"2026_JourNumberTheory_Baranczuk.pdf","creator":"dernst","relation":"main_file","file_size":754810,"file_id":"22396","date_updated":"2026-07-23T11:32:51Z","content_type":"application/pdf","access_level":"open_access"}],"date_created":"2025-07-27T22:01:25Z","date_published":"2026-02-01T00:00:00Z","_id":"20078","publication_identifier":{"issn":["0022-314X"]},"language":[{"iso":"eng"}],"has_accepted_license":"1","month":"02","page":"170-183","year":"2026","status":"public","quality_controlled":"1","fulldoi":"https://doi.org/10.1016/j.jnt.2025.06.001","file_date_updated":"2026-07-23T11:32:51Z","OA_place":"publisher","corr_author":"1","abstract":[{"lang":"eng","text":"Let A be an abelian variety defined over a number field K, E/K be an elliptic curve, and ϕ : A → Em be an isogeny defined over K. Let P ∈ A(K) be such that ϕ(P)=(Q1,..., Qm) with RankZ(⟨Q1,...,Qm⟩)=1. We will study a divisibility sequence related to the point P and show its relation with elliptic divisibility sequences."}],"researchdata_availability":"no","keyword":["Divisibility sequences","Abelian varieties","Elliptic divisibility sequences","Isogenies","Primitive divisors"],"publication_status":"published","day":"01","arxiv":1,"OA_type":"hybrid","author":[{"full_name":"Barańczuk, Stefan","first_name":"Stefan","last_name":"Barańczuk"},{"first_name":"Bartosz","full_name":"Naskręcki, Bartosz","last_name":"Naskręcki"},{"orcid":"0000-0002-0854-0306","first_name":"Matteo","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","full_name":"Verzobio, Matteo","last_name":"Verzobio"}],"article_type":"original","date_updated":"2026-07-23T11:33:57Z","intvolume":"       279","doi":"10.1016/j.jnt.2025.06.001","PlanS_conform":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"publisher":"Elsevier","scopus_import":"1","supplementarymaterial":"no","oa":1,"publication":"Journal of Number Theory","volume":279,"type":"journal_article","das_tickbox":"1","citation":{"chicago":"Barańczuk, Stefan, Bartosz Naskręcki, and Matteo Verzobio. “Divisibility Sequences Related to Abelian Varieties Isogenous to a Power of an Elliptic Curve.” <i>Journal of Number Theory</i>. Elsevier, 2026. <a href=\"https://doi.org/10.1016/j.jnt.2025.06.001\">https://doi.org/10.1016/j.jnt.2025.06.001</a>.","short":"S. Barańczuk, B. Naskręcki, M. Verzobio, Journal of Number Theory 279 (2026) 170–183.","ista":"Barańczuk S, Naskręcki B, Verzobio M. 2026. Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve. Journal of Number Theory. 279, 170–183.","ama":"Barańczuk S, Naskręcki B, Verzobio M. Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve. <i>Journal of Number Theory</i>. 2026;279:170-183. doi:<a href=\"https://doi.org/10.1016/j.jnt.2025.06.001\">10.1016/j.jnt.2025.06.001</a>","mla":"Barańczuk, Stefan, et al. “Divisibility Sequences Related to Abelian Varieties Isogenous to a Power of an Elliptic Curve.” <i>Journal of Number Theory</i>, vol. 279, Elsevier, 2026, pp. 170–83, doi:<a href=\"https://doi.org/10.1016/j.jnt.2025.06.001\">10.1016/j.jnt.2025.06.001</a>.","ieee":"S. Barańczuk, B. Naskręcki, and M. Verzobio, “Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve,” <i>Journal of Number Theory</i>, vol. 279. Elsevier, pp. 170–183, 2026.","apa":"Barańczuk, S., Naskręcki, B., &#38; Verzobio, M. (2026). Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve. <i>Journal of Number Theory</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jnt.2025.06.001\">https://doi.org/10.1016/j.jnt.2025.06.001</a>"},"dataavailabilitystatement":"No data was used for the research described in the article."}]