{"title":"椭圆可整除序列的原始除数的一些有效性结果","authors":"Matteo Verzobio","doi":"10.2140/pjm.2023.325.331","DOIUrl":null,"url":null,"abstract":"Let $P$ be a non-torsion point on an elliptic curve defined over a number field $K$ and consider the sequence $\\{B_n\\}_{n\\in \\mathbb{N}}$ of the denominators of $x(nP)$. We prove that every term of the sequence of the $B_n$ has a primitive divisor for $n$ greater than an effectively computable constant that we will explicitly compute. This constant will depend only on the model defining the curve.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":"25 7","pages":"0"},"PeriodicalIF":0.7000,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Some effectivity results for primitive divisors of elliptic divisibility sequences\",\"authors\":\"Matteo Verzobio\",\"doi\":\"10.2140/pjm.2023.325.331\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $P$ be a non-torsion point on an elliptic curve defined over a number field $K$ and consider the sequence $\\\\{B_n\\\\}_{n\\\\in \\\\mathbb{N}}$ of the denominators of $x(nP)$. We prove that every term of the sequence of the $B_n$ has a primitive divisor for $n$ greater than an effectively computable constant that we will explicitly compute. This constant will depend only on the model defining the curve.\",\"PeriodicalId\":54651,\"journal\":{\"name\":\"Pacific Journal of Mathematics\",\"volume\":\"25 7\",\"pages\":\"0\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-11-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Pacific Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/pjm.2023.325.331\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pacific Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/pjm.2023.325.331","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Some effectivity results for primitive divisors of elliptic divisibility sequences
Let $P$ be a non-torsion point on an elliptic curve defined over a number field $K$ and consider the sequence $\{B_n\}_{n\in \mathbb{N}}$ of the denominators of $x(nP)$. We prove that every term of the sequence of the $B_n$ has a primitive divisor for $n$ greater than an effectively computable constant that we will explicitly compute. This constant will depend only on the model defining the curve.
期刊介绍:
Founded in 1951, PJM has published mathematics research for more than 60 years. PJM is run by mathematicians from the Pacific Rim. PJM aims to publish high-quality articles in all branches of mathematics, at low cost to libraries and individuals. The Pacific Journal of Mathematics is incorporated as a 501(c)(3) California nonprofit.