Matematičeskie zametki, Tome 8 (1970) no. 3, pp. 361-371
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N. I. Fel'dman. Effective bounds for the number of solutions of certain diophantine equations. Matematičeskie zametki, Tome 8 (1970) no. 3, pp. 361-371. http://geodesic.mathdoc.fr/item/MZM_1970_8_3_a8/
@article{MZM_1970_8_3_a8,
author = {N. I. Fel'dman},
title = {Effective bounds for the number of solutions of certain diophantine equations},
journal = {Matemati\v{c}eskie zametki},
pages = {361--371},
year = {1970},
volume = {8},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1970_8_3_a8/}
}
TY - JOUR
AU - N. I. Fel'dman
TI - Effective bounds for the number of solutions of certain diophantine equations
JO - Matematičeskie zametki
PY - 1970
SP - 361
EP - 371
VL - 8
IS - 3
UR - http://geodesic.mathdoc.fr/item/MZM_1970_8_3_a8/
LA - ru
ID - MZM_1970_8_3_a8
ER -
%0 Journal Article
%A N. I. Fel'dman
%T Effective bounds for the number of solutions of certain diophantine equations
%J Matematičeskie zametki
%D 1970
%P 361-371
%V 8
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_1970_8_3_a8/
%G ru
%F MZM_1970_8_3_a8
It is proved that the number of solutions of the diophantine equation $$ \mathrm{Norm}\,(z_1\omega_1+\dots+z_m\omega_m)=f(z_1,\dots,z_m), $$ is finite, where $\omega_1,\dots,\omega_m$ are algebraic numbers of a special type, the left side of the equation is the norm with respect to a quadratic field, and $f$ is a low-degree polynomial.
