Congruent Numbers and Heegner Points
Number Theory
2012-11-01 v1
Abstract
Mohammed Ben Alhocain, in an Arab manuscript of the tenth century, stated that the principal object of the theory of rational right triangles is to find a square which when increased or diminished by a certain number becomes a square (see Dickson). In modern language, this object is to find a rational point of infinite order on the elliptic curve . Heegner constructed (see also Monsky) such rational points in the case that are primes congruent to 5, 7 modulo 8 or twice primes congruent to 6 modulo 8. We extend Heegner's result to integers with many prime divisors.
Keywords
Cite
@article{arxiv.1210.8231,
title = {Congruent Numbers and Heegner Points},
author = {Ye Tian},
journal= {arXiv preprint arXiv:1210.8231},
year = {2012}
}