Higher moments of distances between consecutive Ford spheres
Alan Haynes, Kayleigh Measures
TL;DR
This paper extends previous work on Ford spheres by deriving asymptotic formulas for higher moments of distances between consecutive spheres, utilizing lattice point counting and Gauss circle problem estimates.
Contribution
It introduces new asymptotic formulas for higher moments of distances between Ford spheres, building on prior second moment results.
Findings
Asymptotic formulas for higher moments of distances
Use of lattice point counting with Gauss circle problem error terms
Enhanced understanding of Ford sphere arrangements
Abstract
In previous work the second author derived an asymptotic formula for the sum of the distances between centers of consecutive Ford spheres. In this paper we extend these results by proving asymptotic formulas for higher moments of the distances. Our proofs rely on lattice point counting estimates with error terms coming from the Gauss circle problem.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.