A Diophantine Problem on Elliptic Curves
A Diophantine Problem on Elliptic Curves
This paper examines simultaneous diophantine approximations to coordinates of certain points on a product of elliptic curves. Specifically, let $\wp (z)$ be a Weierstrass elliptic function with algebraic invariants and complex multiplication. Suppose that $\beta$ is cubic over the "field of multiplications" of $\wp (z)$ and that $u \in \mathbb …