2009/08/24 by David Ralston, Ralston, David
Mathematics · #11K38 #Analytic Number Theory Research #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical Dynamics and Fractals #Number Theory (math.NT) #math.DS #math.NT #msc:11K38
paper · pdf · doi:10.48550/arxiv.0908.3469
This paper has been withdrawn by the author. Paper withdrawn - results are replaced and improved in "substitutions and 1/2 discrepancy of {n theta + x}"
openalex publication_date 2009/08/24 · arxiv created 2011/06/03 · arxiv updated 2011/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.