Related papers: On uniform distribution modulo one
We prove some theorems which give sufficient conditions for the existence of prime numbers among the terms of a sequence which has pairwise relatively prime terms.
The Integration Theory of Linear Ordinary Differential Equation.
This paper is concerned with the concept of linear repetitivity in the theory of tilings. We prove a general uniform subadditive ergodic theorem for linearly repetitive tilings. This theorem unifies and extends various known (sub)additive…
In this paper, we establish some theorems on the distribution of primes in higher-order progressions on average.
In this paper, a new calculus on sequences is defined. Also, the $\lambda$-derivative and the $\lambda$-integration are investigated. The fundamental theorem of $\lambda$-calculus is included. A suitable function basis for the…
Distributed representations (such as those based on embeddings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We…
In 1935 J.G. van der Corput introduced a sequence which has excellent uniform distribution properties modulo 1. This sequence is based on a very simple digital construction scheme with respect to the binary digit expansion. Nowadays the van…
In a previous paper we have introduced a class of multiplications of distributions in one dimension. Here we furnish different generalizations of the original definition and we discuss some applications of these procedures to the…
We take some first steps in providing a synthetic theory of distributions. In particular, we are interested in the use of distribution theory as foundation, not just as tool, in the study of the wave equation.
We introduce extremely symmetric primes and provide some elementary properties of these.
We examine the uniform distribution theory of H. Weyl when there is a periodic perturbation present. As opposed to the classical setting, in this case the conditions for (mod 1) density and (mod 1) uniform distribution turn out to be…
We give a new proof of Lucas' Theorem in elementary number theory.
In the first part of this paper the notion of natural metric on the set of natural numbers is defined. It is such metric that the completion of N is a compact metric space that a probability borel measure exists in order that the sequence…
A classical problem in analytic number theory is to study the distribution of $\alpha p$ modulo 1, where $\alpha$ is irrational and $p$ runs over the set of primes. We consider the subsequence generated by the primes $p$ such that $p+2$ is…
We consider the joint distribution of real and imaginary parts of eigenvalues of random matrices with independent entries with mean zero and unit variance. We prove the convergence of this distribution to the uniform distribution on the…
Starting from a study of Y. Bugeaud and A. Dubickas (2005) on a question in distribution of real numbers modulo 1 via combinatorics on words, we survey some combinatorial properties of (epi)Sturmian sequences and distribution modulo 1 in…
We describe the limit zero distributions of sequences of polynomials with positive coefficients.
By using the properties of the uniformly distributed sequences of real numbers on $(0,1)$, a short proof of a certain version of Kolmogorov strong law of large numbers is presented which essentially differs from Kolmogorov's original proof.
We develop an elementary divisor theory for the unimodular and the modular group over quadratic field extensions and quaternion algebras. In particular, we investigate which sets of elementary divisors can occur. Under an additional…
We extend Carleson's interpolation Theorem to sequences of matrices, by giving necessary and sufficient separation conditions for a sequence of matrices to be interpolating.