The metric theory of the pair correlation function for small non‐integer powers

Abstract

For 0 < θ < 1 $0<\theta <1$ , we show that for almost all α $\alpha$ , the pair correlation function of the sequence of fractional parts of { α n θ : n ⩾ 1 } $\lbrace \alpha n^\theta :n\geqslant 1 \rbrace$ is Poissonian.

Locations

• Journal of the London Mathematical Society - View
• arXiv (Cornell University) - View - PDF
• CaltechAUTHORS (California Institute of Technology) - View - PDF