{"acknowledgement":"Silverman, and Paul Voutier for the comments on the earlier version of this paper. The first author acknowledges the support by Dioscuri programme initiated by the Max Planck Society, jointly managed with the National Science Centre (Poland), and mutually funded by the Polish Ministry of Science and Higher Education and the German Federal Ministry of Education and Research. The second author has been supported by MIUR (Italy) through PRIN 2017 ‘Geometric, algebraic and analytic methods in arithmetic’ and has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101034413.","scopus_import":"1","publisher":"Cambridge University Press","oa_version":"Published Version","day":"26","date_updated":"2024-03-13T11:55:21Z","ddc":["510"],"publication_status":"epub_ahead","month":"02","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"date_published":"2024-02-26T00:00:00Z","abstract":[{"text":"In this note, we prove a formula for the cancellation exponent  kv,n between division polynomials  ψn  and  ϕn  associated with a sequence  {nP}n∈N of points on an elliptic curve  E  defined over a discrete valuation field  K. The formula greatly generalizes the previously known special cases and treats also the case of non-standard Kodaira types for non-perfect residue fields.","lang":"eng"}],"has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","status":"public","department":[{"_id":"TiBr"}],"ec_funded":1,"author":[{"last_name":"Naskręcki","full_name":"Naskręcki, Bartosz","first_name":"Bartosz"},{"first_name":"Matteo","full_name":"Verzobio, Matteo","orcid":"0000-0002-0854-0306","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","last_name":"Verzobio"}],"citation":{"chicago":"Naskręcki, Bartosz, and Matteo Verzobio. “Common Valuations of Division Polynomials.” <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>. Cambridge University Press, 2024. <a href=\"https://doi.org/10.1017/prm.2024.7\">https://doi.org/10.1017/prm.2024.7</a>.","ista":"Naskręcki B, Verzobio M. 2024. Common valuations of division polynomials. Proceedings of the Royal Society of Edinburgh Section A: Mathematics., 2203.02015.","short":"B. Naskręcki, M. Verzobio, Proceedings of the Royal Society of Edinburgh Section A: Mathematics (2024).","apa":"Naskręcki, B., &#38; Verzobio, M. (2024). Common valuations of division polynomials. <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/prm.2024.7\">https://doi.org/10.1017/prm.2024.7</a>","ieee":"B. Naskręcki and M. Verzobio, “Common valuations of division polynomials,” <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>. Cambridge University Press, 2024.","ama":"Naskręcki B, Verzobio M. Common valuations of division polynomials. <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>. 2024. doi:<a href=\"https://doi.org/10.1017/prm.2024.7\">10.1017/prm.2024.7</a>","mla":"Naskręcki, Bartosz, and Matteo Verzobio. “Common Valuations of Division Polynomials.” <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>, 2203.02015, Cambridge University Press, 2024, doi:<a href=\"https://doi.org/10.1017/prm.2024.7\">10.1017/prm.2024.7</a>."},"type":"journal_article","year":"2024","date_created":"2023-01-16T11:45:22Z","doi":"10.1017/prm.2024.7","publication":"Proceedings of the Royal Society of Edinburgh Section A: Mathematics","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["2203.02015"]},"quality_controlled":"1","title":"Common valuations of division polynomials","article_type":"original","oa":1,"keyword":["Elliptic curves","Néron models","division polynomials","height functions","discrete valuation rings"],"project":[{"grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1017/prm.2024.7"}],"publication_identifier":{"issn":["0308-2105"],"eissn":["1473-7124"]},"language":[{"iso":"eng"}],"article_number":"2203.02015","_id":"12311"}