On the Hausdorff dimension of some sets of numbers defined through the   digits of their $Q$-Cantor series expansions
  Following in the footsteps of P. Erd\H{o}s and A. R\'enyi we compute the Hausdorff dimension of sets of numbers whose digits with respect to their $Q$-Cantor series expansions satisfy various statistical properties. In particular, we consider difference sets associated with various notions of normality and sets of numbers with a prescribed range of digits. 
Dylan Airey and Bill Mance
math.NT