On a conjecture of Erdös and Szüsz related to uniform distribution mod 1

@article{Kesten1966OnAC,
  title={On a conjecture of Erd{\"o}s and Sz{\"u}sz related to uniform distribution mod 1},
  author={Harry Kesten},
  journal={Acta Arithmetica},
  year={1966},
  volume={12},
  pages={193-212}
}
  • H. Kesten
  • Published 1966
  • Mathematics
  • Acta Arithmetica

Sets of bounded discrepancy for multi-dimensional irrational rotation

We study bounded remainder sets with respect to an irrational rotation of the d-dimensional torus. The subject goes back to Hecke, Ostrowski and Kesten who characterized the intervals with bounded

Exponential Riesz Bases, Discrepancy of Irrational Rotations and BMO

We study the basis property of systems of exponentials with frequencies belonging to ‘simple quasicrystals’. We show that a diophantine condition is necessary and sufficient for such a system to be a

The Surprising Accuracy of Benford’s Law in Mathematics

TLDR
Benford’s law is proved to be an empirical “law” governing the frequency of leading digits in numerical data sets, and the observed behavior is related to classical results in Diophantine approximation as well as recent deep conjectures in this area.

Weighted $$1\times 1$$1×1 Cut-and-Project Sets in Bounded Distance to a Lattice

TLDR
Recent results of Grepstad and Larcher are used to show that weighted cut-and-project sets are bounded distance equivalent to some lattice if the weight function h is continuous on the internal space, and if h is either piecewise linear, or twice differentiable with bounded curvature.

Pinball Dynamics: Unlimited Energy Growth in Switching Hamiltonian Systems

A family of discontinuous symplectic maps arising naturally in the study of nonsmooth switched Hamiltonian systems is considered. This family depends on two parameters and is a canonical model for

On some oscillating sums

This paper deals with various properties (theoretical as well as computational) of the sums Sα(n) = ∑n j=1(−1) where α is any real number (mostly a positive real quadratic). Communicated by Michael

Lattice Bounded Distance Equivalence for 1D Delone Sets with Finite Local Complexity

Spectra of suitably chosen Pisot-Vijayaraghavan numbers represent non-trivial examples of self-similar Delone point sets of finite local complexity, indispensable in quasicrystal modeling. For the

Diophantine properties of IETs and general systems: quantitative proximality and connectivity

AbstractThree properties of dynamical systems (recurrence, connectivity and proximality) are quantified by introducing and studying the gauges (measurable functions) corresponding to each of these

Discovering an infinite prime flow by finding a Proximal Orbit Dense flow

In this document, the proof of the existence of an infinite prime flow, by showing that a Proximal Orbit Dense flow is prime, is examined. This proof has been given by Furstenberg, Keynes and Shapiro
...