Controlled Divergence of Discrepancy Sums

Details Controlled Divergence of Discrepancy Sums Controlled Divergence of Discrepancy Sums

2009-08-24

arxiv.org/abs/0908.3469v3

Mathematics

Number Theory

This paper has been withdrawn by the author. Paper withdrawn - results are replaced and improved in "substitutions and 1/2 dis

Scientific paper

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.

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