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
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020 |a 00029947 (ISSN) 
245 1 0 |a DISTINCT DISTANCES ON HYPERBOLIC SURFACES 
260 0 |b American Mathematical Society  |c 2022 
856 |z View Fulltext in Publisher  |u https://doi.org/10.1090/tran/8603 
520 3 |a 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. 
650 0 4 |a equilateral dimension 
650 0 4 |a Erdos distinct distances 
650 0 4 |a Fuchsian group 
650 0 4 |a hyperbolic surface 
700 1 |a Meng, X.  |e author 
773 |t Transactions of the American Mathematical Society 

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