Geodesic
Approximation to the transcendental relationship of two algebraic points of the function $\wp(z)$ with complex multiplication
Matematičeskie zametki, Tome 20 (1976) no. 1, pp. 47-60 Cet article a éte moissonné depuis la source Math-Net.Ru

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For fixed $\varepsilon>0$, the following inequality holds: $$ \Bigl|\frac uv-\beta\Bigr|>C\exp(-(\ln H)^{2+\varepsilon}) $$ for all numbers $\beta$ belonging to a field $K$ of finite degree over $Q$. The constant $C>0$ does not depend on beta. $H$ is the height of beta. $\wp(u)$ and $\wp(v)$ are algebraic numbers, and $u/v$ is a transcendental number. $\wp(z)$ is the Weierstrass function with complex multiplication and algebraic invariants. The proof is ineffective. 
@article{MZM_1976_20_1_a5,
     author = {N. D. Nagaev},
     title = {Approximation to the transcendental relationship of two algebraic points of the function $\wp(z)$ with complex multiplication},
     journal = {Matemati\v{c}eskie zametki},
     pages = {47--60},
     year = {1976},
     volume = {20},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_20_1_a5/}
}
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N. D. Nagaev. Approximation to the transcendental relationship of two algebraic points of the function $\wp(z)$ with complex multiplication. Matematičeskie zametki, Tome 20 (1976) no. 1, pp. 47-60. http://geodesic.mathdoc.fr/item/MZM_1976_20_1_a5/