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Transactions of the American Mathematical Society

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A Diophantine problem on elliptic curves

Author: Robert Tubbs
Journal: Trans. Amer. Math. Soc. 309 (1988), 325-338
MSC: Primary 11J85
MathSciNet review: 957074
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Abstract: 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{C}$ such that $ \zeta = (\wp (u),\,\wp (\beta u),\,\wp ({\beta ^2}u))$ is defined. We study approximations to $ \zeta $ by points which lie on curves defined over $ \mathbb{Z}$.

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Article copyright: © Copyright 1988 American Mathematical Society