Polynomial effective density in quotient of $\mathrm{SL}_2(\mathbb{Q}_p) \times \mathrm{SL}_2(\mathbb{Q}_p)$

Zuo Lin

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arxiv 2404.13931 v1 pith:NV44EW5K submitted 2024-04-22 math.DS

Polynomial effective density in quotient of SL₂(mathbb{Q}_p) times SL₂(mathbb{Q}_p)

Zuo Lin This is my paper

classification math.DS

keywords mathbbmathrmdensityeffectivepolynomialtheoremtimesambient

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We prove an effective density theorem with polynomial error rate for orbits of upper triangular subgroup of $\mathrm{SL}_2(\mathbb{Q}_p)$ in $\mathrm{SL}_2(\mathbb{Q}_p) \times \mathrm{SL}_2(\mathbb{Q}_p)$ for prime number $p > 3$. The proof is based on the use of Margulis function, a restricted projection theorem on $\mathbb{Q}_p^3$, and spectral gap of the ambient space.

Polynomial effective density in quotient of SL₂(mathbb{Q}_p) times SL₂(mathbb{Q}_p)

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