Geodesic
Transcendence type for almost all points in real $m$-dimensional space
Sbornik. Mathematics, Tome 198 (2007) no. 10, pp. 1443-1463 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $P$ be a polynomial of $m$ variables with integer coefficients, $\deg P$ the total degree of $P$, $H(P)$ the maximum absolute value of the coefficients of $P$, and $t(P)=\deg P+\ln H(P)$ the type of the polynomial $P$. It is shown that for almost all points $\overline\xi\in\mathbb R^m$ (in the sense of Lebesgue $m$-measure) there exists a constant $c=c(\overline\xi)>0$ such that the inequality $\ln\lvert P(\overline\xi)\rvert>-ct(P)^{m+1}$ holds for each polynomial $P\in\mathbb Z[x_1,\dots,x_m]$, $P\not\equiv0$. Bibliography: 13 titles. 
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     title = {Transcendence type for almost all points in real $m$-dimensional space},
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S. V. Mikhailov. Transcendence type for almost all points in real $m$-dimensional space. Sbornik. Mathematics, Tome 198 (2007) no. 10, pp. 1443-1463. http://geodesic.mathdoc.fr/item/SM_2007_198_10_a3/

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