By proving expansion in SL₂(ℤ/qℤ) and applying Shkredov's framework, the paper confirms Zaremba's conjecture.
Expansion and random walks in SL _d( Z /p^n Z ) : I
2 Pith papers cite this work. Polarity classification is still indexing.
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Proves that the Cayley graphs of Zariski-dense subgroups of SL2(Z) x SL2(Z) and SL2(Z) ltimes Z^2 modulo q form expander families.
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Expansion in $\text{SL}_2(\mathbb Z/q\mathbb Z)$ and Zaremba's conjecture
By proving expansion in SL₂(ℤ/qℤ) and applying Shkredov's framework, the paper confirms Zaremba's conjecture.
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Super approximation for $\text{SL}_2\times \text{SL}_2$ and $\text{ASL}_2$
Proves that the Cayley graphs of Zariski-dense subgroups of SL2(Z) x SL2(Z) and SL2(Z) ltimes Z^2 modulo q form expander families.