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math.QA2026
Nuancing the uniqueness of -rationals
Perrine Jouteur, Olga Paris-Romaskevich, Alexander Thomas
We prove uniqueness of -rational numbers up to conjugacy, using character varieties. Despite the uniqueness, we exhibit a two-parameter family of deformations of rationals with…
math.QA2026
Plane geometry of -rationals and Springborn Operations
Perrine Jouteur, Olga Paris-Romaskevich, Alexander Thomas
We study the geometry of -rational numbers, introduced by Morier-Genoud and Ovsienko, for positive real . In particular, we construct and analyse the deformed Farey triangula…