Elliptic curves and continued fractions
Number Theory
2023-03-24 v6 Operator Algebras
Abstract
It is proved that the rank of an elliptic curve is one less the arithmetic complexity of the corresponding non-commutative torus. As an illustration, we consider a family of elliptic curves with complex multiplication.
Keywords
Cite
@article{arxiv.1611.00278,
title = {Elliptic curves and continued fractions},
author = {Igor V. Nikolaev},
journal= {arXiv preprint arXiv:1611.00278},
year = {2023}
}
Comments
to appear in Aequationes Mathematicae