Related papers: On uniform distribution modulo one

The purpose of this note is to give an accessible proof of Moliens Theorem in Invariant Theory, in the language of today's Linear Algebra and Group Theory, in order to prevent this beautiful theorem from being forgotten.

A pattern of a sequence is a sequence of integer indices with each index describing the order of first occurrence of the respective symbol in the original sequence. In a recent paper, tight general bounds on the block entropy of patterns of…

Finding the underlying probability distributions of a set of observed sequences under the constraint that each sequence is generated i.i.d by a distinct distribution is considered. The number of distributions, and hence the number of…

In this paper, the notion of a uniformly distributed systems of elements on the variety of metabelian Lie algebras is introduced. This notion is analogous to one of a measure preserving systems of elements on group varieties. As the main…

In this paper we give a simple, short, and self-contained proof for a non-trivial upper bound on the probability that a random $\pm 1$ symmetric matrix is singular.

We study odd numbers through a straightforward indexing. We focus in particular on odd prime and composite numbers and their distribution. With a counting argument, we calculate the limit of two sums and compare their convergence rate.

Uniform interpolation is a strengthening of interpolation that holds for certain propositional logics. The starting point of this chapter is a theorem of A. Pitts, which shows that uniform interpolation holds for intuitionistic…

We give a constructive, metastable formulation of a theorem about the exchange of limits for convergent sequence $L^1$ functions. A crucial tool is a one-dimensional version of Szemeredi's regularity lemma for $L^1$ functions.

In this note we provide a simple formula of general term of recurrent sequence.

We discuss a version of the fundamental theorem of calculus in several variables and some applications, of potential interest as a teaching material in undergraduate courses.

I give a proof of the uniform boundedness theorem that is elementary (i.e. does not use any version of the Baire category theorem) and also extremely simple.

In the paper, the occurrence of zeros and ones in the binary expansion of the primes is studied. In particular the statement in the title is established. The proof is unconditional.

The aim of the present article is to introduce a concept which allows to generalise the notion of Poissonian pair correlation, a second-order equidistribution property, to higher dimensions. Roughly speaking, in the one-dimensional setting,…

The theory of equidistribution is about hundred years old, and has been developed primarily by number theorists and theoretical computer scientists. A motivated uninitiated peer could encounter difficulties perusing the literature, due to…

We obtain statistical results on the possible distribution of all partial sums of a Kloosterman sum modulo a prime, by computing explicitly the support of the limiting random Fourier series of our earlier functional limit theorem for…

We develop a theory of modulus triples, for future motivic applications.

Assuming the Generalized Riemann Hypothesis we obtain uniform, effective number-field analogues of Mertens' theorems.

In this note we classify sequences according to whether they are morphic, pure morphic, uniform morphic, pure uniform morphic, primitive morphic, or pure primitive morphic, and for each possibility we either give an example or prove that no…

We have extended recently proposed model of parton distribution i nucleons to the case of nucleons in nuclei.

We propose a framework for model-theoretic stability and simplicity in an approximate first-order setting and generalize some classical results.