Monotone subsequences in the sequence of fractional parts of multiples of an irrational.
Nombres algébriques et substitutions
Note on sequences well-spaced and well-distributed among congruence classes
Nouvelles caractérisations des nombres de Pisot et de Salem
On a distribution problem in finite sets
On a result of Mahler on the decimal expansions of (nα)
On absolute (j, ε)-normality in the rational fractions with applications to normal numbers
On density modulo 1 of some expressions containing algebraic integers
On families of Pisot -sequences
On generalised arithmetic and geometric progressions
On irregularities of distribution, III
On irregularities of distribution, IV
On limit points of subsequences of uniformly distributed sequences
Given a subsequence of a uniformly distributed sequence, relations between the asymptotic densities of sets of its indices and the Lebesgue measure of the set of all its limit points are studied.
On normal numbers and powers of algebraic numbers.
On Riemann Sums and Lebesgue Integrals.
On the convergence to 0 of mₙξmod 1
We show that for any irrational number α and a sequence of integers such that , there exists a continuous measure μ on the circle such that . This implies that any rigidity sequence of any ergodic transformation is a rigidity sequence for some weakly mixing dynamical system. On the other hand, we show that for any α ∈ ℝ - ℚ, there exists a sequence of integers such that and such that is dense on the circle if and only if θ ∉ ℚα + ℚ.
On the discrepancy of (nα)
On the discrepancy of sequences associated with the sum-of-digits function
If denotes the sequence of best approximation denominators to a real , and denotes the sum of digits of in the digit representation of to base , then for all irrational, the sequence is uniformly distributed modulo one. Discrepancy estimates for the discrepancy of this sequence are given, which turn out to be best possible if has bounded continued fraction coefficients.
On the distributation of p ... modulo one.
On the distribution function of certain sequences (mod 1)