31 citations · 81 across the 30 of their papers we have counts for
45 papers
Convergence of Fourier--Bohr coefficients for regular Euclidean model sets
Michael Baake, Alan Haynes
It is well known that the Fourier--Bohr coefficients of regular model sets exist and are uniformly converging, volume-averaged exponential sums. Several proofs for this statement a…
Expected value of the smallest denominator in a random interval of fixed radius
Huayang Chen, Alan Haynes
We compute the probability mass function of the random variable which returns the smallest denominator of a reduced fraction in a randomly chosen real interval of radius . As…
A three gap theorem for the adeles
Akshat Das, Alan Haynes
We prove a natural generalization of the classical three gap theorem, for rotations on adelic tori. Our proof is an adaptation to the adeles of the lattice based approach to gaps p…
Higher dimensional gap theorems for the maximum metric
Alan Haynes, Juan J. Ramirez
Recently, the first author together with Jens Marklof studied generalizations of the classical three distance theorem to higher dimensional toral rotations, giving upper bounds in…
A five distance theorem for Kronecker sequences
Alan Haynes, Jens Marklof
The three distance theorem (also known as the three gap theorem or Steinhaus problem) states that, for any given real number and integer , there are at most three values for…
Level spacing statistics for the multi-dimensional quantum harmonic oscillator: algebraic case
Alan Haynes, Roland Roeder
We study the statistical properties of the spacings between neighboring energy levels for the multi-dimensional quantum harmonic oscillator that occur in a window of fix…