[{"researchdata_availability":"no","keyword":["Divisibility sequences","Abelian varieties","Elliptic divisibility sequences","Isogenies","Primitive divisors"],"publication_status":"published","day":"01","arxiv":1,"fulldoi":"https://doi.org/10.1016/j.jnt.2025.06.001","OA_place":"publisher","file_date_updated":"2026-07-23T11:32:51Z","corr_author":"1","abstract":[{"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.","lang":"eng"}],"article_type":"original","OA_type":"hybrid","author":[{"first_name":"Stefan","full_name":"Barańczuk, Stefan","last_name":"Barańczuk"},{"last_name":"Naskręcki","full_name":"Naskręcki, Bartosz","first_name":"Bartosz"},{"first_name":"Matteo","full_name":"Verzobio, Matteo","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","orcid":"0000-0002-0854-0306","last_name":"Verzobio"}],"scopus_import":"1","publisher":"Elsevier","oa":1,"supplementarymaterial":"no","intvolume":"       279","date_updated":"2026-07-23T11:33:57Z","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)"},"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>.","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>.","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.","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.","publication":"Journal of Number Theory","volume":279,"type":"journal_article","das_tickbox":"1","oa_version":"Published Version","title":"Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve","isi":1,"external_id":{"arxiv":["2309.09699"],"isi":["001541172400002"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"Yes (via OA deal)","file":[{"file_size":754810,"relation":"main_file","date_updated":"2026-07-23T11:32:51Z","content_type":"application/pdf","file_id":"22396","access_level":"open_access","date_created":"2026-07-23T11:32:51Z","success":1,"checksum":"34e6e965a2b30a258e0d4103350a68fd","file_name":"2026_JourNumberTheory_Baranczuk.pdf","creator":"dernst"}],"date_created":"2025-07-27T22:01:25Z","date_published":"2026-02-01T00:00:00Z","department":[{"_id":"TiBr"}],"ddc":["500"],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0022-314X"]},"has_accepted_license":"1","month":"02","_id":"20078","year":"2026","status":"public","quality_controlled":"1","page":"170-183"}]