Published January 11, 2019
| Version Submitted + Published
Journal Article
Open
On Cartesian Products which Determine Few Distinct Distances
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Abstract
Every set of points P determines Ω(|P|/log|P|) distances. A close version of this was initially conjectured by Erdős in 1946 and rather recently proved by Guth and Katz. We show that when near this lower bound, a point set P of the form A×A must satisfy |A−A|≪|A|2−2/7log1/7|A| This improves recent results of Hanson and Roche-Newton.
Additional Information
© 2019 The author. Released under the CC BY-ND license (International 4.0). Submitted: Mar 21, 2018; Accepted: Nov 18, 2018; Published: Jan 11, 2019. I would like to thank Oliver Roche-Newton, Misha Rudnev and Adam Sheffer for helpful conversations.Attached Files
Published - 7736-PDF_file-26795-2-10-20190106.pdf
Submitted - 1612.06153.pdf
Files
1612.06153.pdf
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Identifiers
- Eprint ID
- 92774
- Resolver ID
- CaltechAUTHORS:20190207-160429913
Related works
- Describes
- https://arxiv.org/abs/1612.06153 (URL)
Dates
- Created
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2019-02-08Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field