On the asymptotic distribution of the powers of -matrices
On the Boundedness of Weyl Sums.
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 diaphony of some finite hybrid point sets
On the discrepancy estimate of normal numbers
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 distribution function of certain sequences (mod 1)
On the distribution of argL(s,χ) in the half-plane σ > ½
On the distribution of modulo one
In this paper, we give a new upper-bound for the discrepancyfor the sequence , when and .
On the distribution of s-dimensional Kronecker-sequences
On the Distribution of Sequences connected with Digit-Representation.
On the Distribution of Sequences Connected with Good Lattice Points.
On the distribution of the distances of multiples of an irrational number to the nearest integer
On the Existence of Uniformly Distributed Sequences in Compact Topological Spaces II.
On the existence of uniformly distributed sequences in compact spaces
On the fractional parts of and related sequences. I
This paper and its sequels deal with a new concept of distributions modulo one which is connected with the Dirichlet divisor and similar problems. Each of the theorems has some independent interest, and in addition some of the techniques developed lead to improvements in certain applications of the hyperbola method.
On the frequency of small fractional parts in certain real sequences, IV
On the discrepancy of distances of points from a finite sequence