Diffraction of the primes and other sets of zero density

Abstract

In this paper, we show that the diffraction of the primes is absolutely continuous, showing no bright spots (Bragg peaks). We introduce the notion of counting diffraction, extending the classical notion of (density) diffraction to sets of density zero. We develop the counting diffraction theory and give many examples of sets of zero density of all possible spectral types.

37 pages, final version, accepted to Journal of the Australian Mathematical Society

References in corpus (6)

• Dynamical systems on translation bounded measures: Pure point dynamical and diffraction spectra
• Dynamics on the graph of the torus parametrisation
• On the Fourier Analysis of Measures with Meyer Set Support
• Uncovering Multiscale Order in the Prime Numbers via Scattering
• Periods and factors of weak model sets
• Some comments on pinwheel tilings and their diffraction