On hyperbolic once-punctured tori the multiplicity of any simple geodesic length L is at most C (log L)^2, improving prior logarithmic bounds for Markoff numbers.
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McShane-Rivin norm balls and simple-length multiplicities
On hyperbolic once-punctured tori the multiplicity of any simple geodesic length L is at most C (log L)^2, improving prior logarithmic bounds for Markoff numbers.