Geodesic
Order function for almost all numbers
Matematičeskie zametki, Tome 15 (1974) no. 3, pp. 405-414

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For almost all pointsxgrexist $\xi\in R^m$ ($m>2$) the inequality $$ \sup\ln\frac1{|P(\xi)|}\ll(\ln u)^{m+2}, $$ is valid, where the upper bound is taken over all nonzero polynomials $P$ for which $\exp(\operatorname{deg}P)L(P)$ where $L(P)$ is the sum of the moduli of the coefficients of $P$. When $m=1$ the exponent of the right side is equal to 2. 
@article{MZM_1974_15_3_a6,
     author = {Yu. V. Nesterenko},
     title = {Order function for almost all numbers},
     journal = {Matemati\v{c}eskie zametki},
     pages = {405--414},
     publisher = {mathdoc},
     volume = {15},
     number = {3},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_15_3_a6/}
}
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Yu. V. Nesterenko. Order function for almost all numbers. Matematičeskie zametki, Tome 15 (1974) no. 3, pp. 405-414. http://geodesic.mathdoc.fr/item/MZM_1974_15_3_a6/