The rank of a CM elliptic curve and a recurrence formula

Autor:	Keiichiro Nomoto
Rok vydání:	2022
Předmět:	Polynomial Algebra and Number Theory Conjecture Mathematics - Number Theory 11F67 11G40 Mathematics::Number Theory Recurrence formula Modulo Prime number Constant term Combinatorics Elliptic curve FOS: Mathematics Rank (graph theory) Number Theory (math.NT) Mathematics
Zdroj:	Journal of Number Theory. 238:60-81
ISSN:	0022-314X
Popis:	Let $p$ be a prime number and $E_{p}$ denote the elliptic curve $y^2=x^3+px$. It is known that for $p$ which is congruent to $1, 9$ modulo $16$, the rank of $E_{p}$ over $\mathbb{Q}$ is equal to $0, 2$. Under the condition that the Birch and Swinnerton-Dyer conjecture is true, we give a necessary and sufficient condition that the rank is $2$ in terms of the constant term of some polynomial that is defined by a recurrence formula. Comment: 16 pages
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9eac9bc32cf230375dfe29a8d246adf6 https://doi.org/10.1016/j.jnt.2021.08.003 Zobrazit plný text záznamu Full Text from ScienceDirect