On distribution functions of ξ(3/2)ⁿ mod 1
On exceptional systems of random integers.
On existence and discrepancy of certain digital Niederreiter-Halton sequences
On finite pseudorandom binary sequences VII: The measures of pseudorandomness
On some remarkable properties of the two-dimensional Hammersley point set in base 2
We study a special class of -nets in base 2. In particular, we are concerned with the two-dimensional Hammersley net that plays a special role among these since we prove that it is the worst distributed with respect to the star discrepancy. By showing this, we also improve an existing upper bound for the star discrepancy of digital -nets over . Moreover, we show that nets with very low star discrepancy can be obtained by transforming the Hammersley point set in a suitable way.
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 diaphony of one class of one-dimensional sequences.
On the distribution of the sequence (nα) with transcendental α
On the fractional parts of the natural powers of a fixed number.
On the range of fractional parts {ξ(p/q)ⁿ}
On the set .
Poincaré's conjecture and the distribution of digits in tables
Polynomials Involving the Floor Function.
Propriétés ergodiques des suites -multiplicatives
Quelques remarques sur la répartition modulo 1 de la suite
Quelques résultats nouveaux sur les fonctions additives
Relative Gleichverteilung in lokalkompakten Räumen II.
Remarks on several types of convergence of bounded sequences
In this paper we analyze relations among several types of convergences of bounded sequences, in particulars among statistical convergence, -convergence, -convergence, almost convergence, strong -Cesàro convergence and uniformly strong -Cesàro convergence.
Répartition modulo 1 dans un corps de séries formelles sur un corps fini [Book]
Répartition modulo 1 de la suite