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 distance between generalized Fibonacci numbers
For an integer k ≥ 2, let be the k-Fibonacci sequence which starts with 0,..., 0,1 (k terms) and each term afterwards is the sum of the k preceding terms. This paper completes a previous work of Marques (2014) which investigated the spacing between terms of distinct k-Fibonacci sequences.
On the distributation of p ... modulo one.
On the distribution function of certain sequences (mod 1)
On the distribution modulo 1 of the sequence
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 Sequences Connected with Good Lattice Points.
On the distribution of the distances of multiples of an irrational number to the nearest integer
On the distribution of the sequence (nα) with transcendental α
On the error term in multidimensional diophantine approximation
On the existence of uniformly distributed sequences in compact spaces
On the exponential local-global principle
Skolem conjectured that the "power sum" A(n) = λ₁α₁ⁿ + ⋯ + λₘαₘⁿ satisfies a certain local-global principle. We prove this conjecture in the case when the multiplicative group generated by α₁,...,αₘ is of rank 1.
On the family of diophantine triples .
On the fractional parts of cubic forms
On the fractional parts of the powers of a rational number
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 fractional parts of and related sequences. II
As promised in the first paper of this series (Ann. Inst. Fourier, 26-4 (1976), 115-131), these two articles deal with the asymptotic distribution of the fractional parts of where is an arithmetical function (namely , , ) and is an integer (or a prime order) running over the interval . The results obtained are rather sharp, although one can improve on some of them at the cost of increased technicality. Number-theoretic applications will be given later on.
On the frequency of small fractional parts in certain real sequences, IV
On the gaps of the Lagrange spectrum