EuDML | Browse

Let $T : ℝ / ℤ \to ℝ / ℤ$ be a von Neumann-Kakutani $q$ - adic adding machine transformation and let $ϕ \in C^{1} ([0, 1])$ . Put $ϕ_{n} (x) : = ϕ (x) + ϕ (T x) + ... + ϕ (T^{n - 1} x), x \in ℝ / ℤ, n \in ℕ .$ We study three questions:1. When will $(ϕ_{n} (x))_{n \geq 1}$ be bounded?2. What can be said about limit points of $(ϕ_{n} (x))_{n \geq 1} ?$ 3. When will the skew product $(x, y) \mapsto (T x, y + ϕ (x))$ be ergodic on $ℝ / ℤ \times ℝ ?$

On $G$ -discrepancy and mixed Monte Carlo and quasi-Monte Carlo sequences.

Gnewuch, Michael, Roşca, Alin V. (2009)

Acta Universitatis Apulensis. Mathematics - Informatics

On infinite series representations of real numbers

János Galambos (1973)

Compositio Mathematica

On integer points in polygons

Maxim Skriganov (1993)

Annales de l'institut Fourier

The phenomenon of anomaly small error terms in the lattice point problem is considered in detail in two dimensions. For irrational polygons the errors are expressed in terms of diophantine properties of the side slopes. As a result, for the $t$ -dilatation, $t \to \infty$ , of certain classes of irrational polygons the error terms are bounded as $≪ ℓ n^{q} t$ with some $q > 0$ , or as $≪ t^{ϵ}$ with arbitrarily small $ϵ > 0$ .

Currently displaying 41 – 60 of 214

Previous Page 3 Next

Displaying 41 – 60 of 214

On distribution functions of sequences generated by scalar and mixed product

On distribution functions of ξ(3/2)ⁿ mod 1

On distribution of sequences of integers

On Ergodic Theory of A. Schmidt's Complex Continued Fractions over Gaussian Field.

On exceptional systems of random integers.

On existence and discrepancy of certain digital Niederreiter-Halton sequences

On exponents of convergence of subsequences

On finite pseudorandom binary sequences I: Measure of pseudorandomness, the Legendre symbol

On finite pseudorandom binary sequences III: The Liouville function, I

On finite pseudorandom binary sequences IV: The Liouville function, II

On finite pseudorandom binary sequences VII: The measures of pseudorandomness

On functions with bounded remainder

On $G$ -discrepancy and mixed Monte Carlo and quasi-Monte Carlo sequences.

On infinite series representations of real numbers

On integer points in polygons

On irregularities of distribution, III

On Irregularities of Distribution in Shifts and Dilations of Integer Sequences. I.

On irregularities of distribution, IV

On irregularities of sums of integers

On isolated, respectively consecutive large values of arithmetic functions

Currently displaying 41 – 60 of 214