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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_20_1_a5/}
}
TY  - JOUR
AU  - N. D. Nagaev
TI  - Approximation to the transcendental relationship of two algebraic points of the function $\wp(z)$ with complex multiplication
JO  - Matematičeskie zametki
PY  - 1976
SP  - 47
EP  - 60
VL  - 20
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1976_20_1_a5/
LA  - ru
ID  - MZM_1976_20_1_a5
ER  - 
%0 Journal Article
%A N. D. Nagaev
%T Approximation to the transcendental relationship of two algebraic points of the function $\wp(z)$ with complex multiplication
%J Matematičeskie zametki
%D 1976
%P 47-60
%V 20
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1976_20_1_a5/
%G ru
%F MZM_1976_20_1_a5
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/