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Rank-one Quadratic Twists of an Infinite Family of Elliptic Curves by Dongho Byeon; Daeyeol Jeon; Chang Heon Kim is a Mathematics article available to read on EtoBox.

What is Rank-one Quadratic Twists of an Infinite Family of Elliptic Curves about?

A conjecture of Goldfeld implies that a positive proportion of quadratic twists of an elliptic curve E=Q has (analytic) rank 1. This assertion has been confirmed by Vatsal [V1] and the first author [By] for only two elliptic curves. Here we confirm this assertion for infinitely many elliptic curves E=Q using the Heegner divisors, the 3-part of the class groups of quadratic fields, and a variant of the binary Goldbach problem for polynomials.

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Author

Dongho Byeon; Daeyeol Jeon; Chang Heon Kim

Publisher

Walter de Gruyter GmbH & Co. KG; Walter de Gruyter GmbH (ISSN 0075-4102)

Published

2009

Language

EN

Field

Mathematics (Physical Sciences)