Abstract
By a classical theorem of Koksma the sequence of fractional parts ({x n}) n≥1 is uniformly distributed for almost all values of x > 1. In the present paper we obtain an exact quantitative version of Koksma’s theorem, by calculating the precise asymptotic order of the discrepancy of ({ξxsn})n⩾1 for typical values of x (in the sense of Lebesgue measure). Here ξ > 0 is an arbitrary constant, and (s n ) n≥1 can be any increasing sequence of positive integers
Original language | English |
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Pages (from-to) | 155-197 |
Journal | Israel Journal of Mathematics |
Volume | 204 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2014 |
Fields of Expertise
- Sonstiges