Order function for almost all numbers
Matematičeskie zametki, Tome 15 (1974) no. 3, pp. 405-414
Citer cet article
Voir la notice de l'article provenant de la source Math-Net.Ru
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.