形式级数域上Engel级数展式中“数字”次数的增长速度

The Growth Rate of the Degrees of the “digits” Occurring in Engel Series Expansions Over the Field of Formal Laurent Series

WU在2003年研究了形式级数域上Engel级数展式中"数字"的次数以线性速度增长的例外集,并利用质量分布原理证明了该例外集具有满Hausdorff维数.本文我们主要研究形式级数域上Engel级数展式中"数字"的次数以多项式和指数速度增长的例外集,并给出他们的Hausdorff维数估计.

WU in 2003 studied the exceptional sets of Engel series expansions in which the degrees of the digits grow with linear orders over the field of formal Laurent series, and proved the exceptional sets have full Hausdorff dimension by using the mass distribution principle. In this paper, we consider the exceptional sets of Engel series expansions in which the degrees of the digits grow with polynomial or exponential orders over the field of formal Laurent series, and we give the estimation of their Haudorff dimensions.