Matematičeskie zametki, Tome 20 (1976) no. 1, pp. 47-60
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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/
@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/}
}
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
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
%U http://geodesic.mathdoc.fr/item/MZM_1976_20_1_a5/
%G ru
%F MZM_1976_20_1_a5
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.
