Geodesic
A metric theorem on the simultaneous approximation of a~zero by the values of integral polynomials
Izvestiya. Mathematics , Tome 16 (1981) no. 1, pp. 21-40.

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In this paper it is proved that the inequality $$ \prod_{i=1}^k|P(\omega_i)|^{-n+k-1-\varepsilon} $$ has only a finite number of solutions in integral polynomials $P(x)$ for almost all $\overline\omega=(\omega_1,\dots,\omega_k)$. Here $H$ is the coefficient of $P(x)$ largest in absolute value. Sprindzuk's conjecture is thereby proved. Bibliography: 7 titles. 
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V. I. Bernik. A metric theorem on the simultaneous approximation of a~zero by the values of integral polynomials. Izvestiya. Mathematics , Tome 16 (1981) no. 1, pp. 21-40. http://geodesic.mathdoc.fr/item/IM2_1981_16_1_a1/

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[3] Sprindzhuk V. G., Metricheskie teoremy o diofantovykh priblizheniyakh i priblizheniyakh algebraicheskimi elementami ogranichennoi stepeni, dissertatsiya, LGU im. A. A. Zhdanova, 1963

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[7] Wirsing E., “Approximation mit algebraischen Zahlen beschrankten Grades”, J. reine und angewandte Math., 206:1–2 (1961), 67–77 | MR | Zbl