On the class number divisibility of pairs of quadratic fields obtained from points on elliptic curves
| Autor: | Yutaka Konomi, Yoshichika Iizuka, Shin Nakano |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
class number quadratic field General Mathematics Mathematics::Number Theory 010102 general mathematics 11R29 010103 numerical & computational mathematics Divisibility rule Isotropic quadratic form 01 natural sciences Prime (order theory) Combinatorics Elliptic curve point multiplication Elliptic curve 11R11 Integer Binary quadratic form Quadratic field 0101 mathematics 11G05 Mathematics elliptic curve |
| Zdroj: | J. Math. Soc. Japan 68, no. 2 (2016), 899-915 |
| Popis: | Let $l$ be the prime $3,5$ or $7$ and let $m$ be a nonzero integer. We give a method for constructing an infinite family of pairs of quadratic fields ${\mathbb Q} \bigl(\sqrt D \big)$ and ${\mathbb Q} \bigl(\sqrt{mD} \big)$ with both class numbers divisible by $l$. Such quadratic fields are parametrized by rational points on a specified elliptic curve. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|