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math.NT2026
Expansion in and Zaremba's conjecture
Xin Zhang
We establish an expansion theory for . Incorporating this into a framework recently developed by Shkredov, we confirm Zaremba's conjecture.
math.NT2016
On Representation of Integers from Thin Subgroups of SL(2,Z) with Parabolics
Xin Zhang
Let be a finitely generated, non-elementary Fuchsian group of the second kind, and be two primitive vectors in . We consider the set…