On a conjecture of Gross and Zagier
Number Theory
2015-11-03 v2
Abstract
Gross and Zagier conjectured that if the analytic rank of a rational elliptic curve is 1, then the order of the rational torsion subgroup of the elliptic curve divides the product of Tamagawa number, Manin constant, and the square root of the order of Tate--Shafarevich group over an imaginary quadratic field. In this paper, we show that this conjecture is true.
Keywords
Cite
@article{arxiv.1501.06296,
title = {On a conjecture of Gross and Zagier},
author = {Dongho Byeon and Taekyung Kim and Donggeon Yhee},
journal= {arXiv preprint arXiv:1501.06296},
year = {2015}
}
Comments
22 pages; major revision: proved the whole conjecture without any other conjecture, deleted some routine computations (will be given upon request)