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The Erdős–Ulam problem, Lang's conjecture and uniformity

The Erdős–Ulam problem, Lang's conjecture and uniformity A rational distance set is a subset of the plane such that the distance between any two points is a rational number. We show, assuming Lang's conjecture, that the cardinalities of rational distance sets in general position are uniformly bounded, generalizing results of Solymosi–de Zeeuw, Makhul–Shaffaf, Shaffaf and Tao. In the process, we give a criterion for certain varieties with non‐canonical singularities to be of general type. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

The Erdős–Ulam problem, Lang's conjecture and uniformity

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References (19)

Publisher
Wiley
Copyright
© 2020 London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms.12381
Publisher site
See Article on Publisher Site

Abstract

A rational distance set is a subset of the plane such that the distance between any two points is a rational number. We show, assuming Lang's conjecture, that the cardinalities of rational distance sets in general position are uniformly bounded, generalizing results of Solymosi–de Zeeuw, Makhul–Shaffaf, Shaffaf and Tao. In the process, we give a criterion for certain varieties with non‐canonical singularities to be of general type.

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Dec 1, 2020

Keywords: ; ; ;

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