Some sums of two rational cubes

Authors
Citation
Dr. Coward, Some sums of two rational cubes, Q J MATH, 51, 2000, pp. 451-464
Citations number
13
Categorie Soggetti
Mathematics
Journal title
QUARTERLY JOURNAL OF MATHEMATICS
ISSN journal
00335606 → ACNP
Volume
51
Year of publication
2000
Part
4
Pages
451 - 464
Database
ISI
SICI code
0033-5606(200012)51:<451:SSOTRC>2.0.ZU;2-K
Abstract
This paper establishes the result that numbers of the shape 5(2)p(p = 2 mod 9) and 5(2)p(2)(p = 5 mod 9), where p a prime, are expressible as the sum of two rational cubes by finding modular parametrizations of the correspond ing elliptic curves, picking special complex points on the curve and manipu lating them to produce rational points thereon.