关于多项式小分数部分的一个注解(英文)

A Remark on Small Fractional Parts of Polynomials

设f(x)为任意一实系数多项式,N.G.Moshchevitin在他的文章[8]中给出了集合{α∈R∶lim infn→∞ nlog n‖αf(n)‖>0}的Hausdorff维数的下界.在本文中,我们延用文[8]的方法并结合齐次Moran集的维数理论给出这个集合Hausdorff维数的精确值.

For any real polynomial f（x）∈R[x],N.G.Moshchevitin[8] estimated the lower bound of the Hausdorff dimension of the set {α∈R∶lim infn→∞ n log n‖αf（n）‖0}.In this paper we give its exact Hausdorff dimension.Our result is based on the method of N.G.Moshchevitin and a basic dimensional result of the homogeneous Moran set.