UNIFORM EQUIPARTITION TEST BOUNDS FOR MULTIPLY SEQUENCES
Marco D. Pollanen · International Journal of Pure and Apllied Mathematics · 2011
For almost all x0 ∈ (0,1), the multiply sequence xn = axn 1 mod 1, with a > 1 an integer, is equidistributed. In this paper we show that equidis- tributed multiply sequences are not m-equipartitioned for any m > 2. We also provide uniform asymptotic bounds for equipartition tests for such sequences.