Poissonian pair correlation on manifolds via the heat kernel
Number Theory
2019-08-08 v2 Classical Analysis and ODEs
Abstract
We define a notion of Poissonian pair correlation (PPC) for Riemannian manifolds without boundary and prove that PPC implies uniform distribution in this setting. This extends earlier work by Grepstad and Larcher, Aistleitner, Lachmann, and Pausinger, Steinerberger, and Marklof.
Cite
@article{arxiv.1904.08286,
title = {Poissonian pair correlation on manifolds via the heat kernel},
author = {Peter J. Grabner and Tetiana A. Stepanyuk},
journal= {arXiv preprint arXiv:1904.08286},
year = {2019}
}
Comments
There is a serious mistake in the proof of Proposition 1