USING ELLIPTIC CURVES TO PRODUCE QUADRATIC NUMBER FIELDS OF HIGH THREE-RANK

We use a connection between the arithmetic of elliptic curves of the form y² = x³ + k and the arithmetic of the quadratic number fields Q(√k) and Q(√-3k) to look for quadratic fields with high three-rank. We give a geometric proof of known results on polynomials that give rise to infinite families o...

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Veröffentlicht in:	The Rocky Mountain journal of mathematics 2004-06, Vol.34 (2), p.599-618
1. Verfasser:	DELONG, MATT
Format:	Artikel
Sprache:	eng
Schlagworte:	11G05 11R29 Arithmetic Curves Integers Mathematical lattices Mathematical theorems Number theory Numbers Polynomials Series convergence
Online-Zugang:	Volltext
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