On the existence of uniformly distributed sequences in compact spaces
On the fractional parts of cubic forms
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 limit points of the fractional parts of powers of Pisot numbers
We consider the sequence of fractional parts , , where is a Pisot number and is a positive number. We find the set of limit points of this sequence and describe all cases when it has a unique limit point. The case, where and the unique limit point is zero, was earlier described by the author and Luca, independently.
On the problem
On the sets of uniqueness of a distribution function of {ξ(p/q)ⁿ}
On the uniform ε-distribution of residues within the periods of rational fractions with applications to normal numbers
On well distribution modulo 1 and systems of numeration