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We prove a quantitative version of the following statement: the unipotentflow orbit of a typical lattice in$\rm{SL}_2(\mathbb{R})/\rm{SL}_2(\mathbb{Z})$ is dense. Our quantitative resultuses A. Weil's bounds for Kloostermann sums.

A note on Diophatine approximation in $\rm{SL}_2(\mathbb{R})$