Controlled Divergence of Discrepancy Sums
arXiv:0908.3469
Abstract
Answering an informal question of K. Park, we show that by fixing some irrational alpha to have a particular standard continued fraction expansion, we may force the associated discrepancy sequences for all x in [0,1), which track the difference between the number of values in the orbit of x under rotation by alpha (modulo one) less than one half versus the number larger than one half, to have maximal values which grow at a prescribed rate.
This paper has been withdrawn by the author. Paper withdrawn - results are replaced and improved in "substitutions and 1/2 discrepancy of {n theta + x}"