DISTINCT DISTANCES ON HYPERBOLIC SURFACES

DISTINCT DISTANCES ON HYPERBOLIC SURFACES

For any cofinite Fuchsian group Γ ⊂PSL(2,R), we show that any set of N points on the hyperbolic surface Γ\H2 determines ≥ CΓ N logN distinct distances for some constant CΓ > 0 depending only on Γ. In particular, for Γ being any finite index subgroup of PSL(2, Z) with μ = [PSL(2, Z) : Γ] < ∞, a...

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Bibliographic Details
Main Author: Meng, X. (Author)
Format: Article
Language:English
Published: American Mathematical Society 2022
Subjects:
equilateral dimension
Erdos distinct distances
Fuchsian group
hyperbolic surface
Online Access:View Fulltext in Publisher
Description
Summary:For any cofinite Fuchsian group Γ ⊂PSL(2,R), we show that any set of N points on the hyperbolic surface Γ\H2 determines ≥ CΓ N logN distinct distances for some constant CΓ > 0 depending only on Γ. In particular, for Γ being any finite index subgroup of PSL(2, Z) with μ = [PSL(2, Z) : Γ] < ∞, any set of N points on Γ\H2 determines ≥ C N μ logN distinct distances for some absolute constant C > 0. © 2022 American Mathematical Society.
ISBN:00029947 (ISSN)
DOI:10.1090/tran/8603

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