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We study an extreme value distribution for the unipotent flow on the modularsurface $\mathrm{SL}_2(\mathbb{R})/\mathrm{SL}_2(\mathbb{Z})$. Using tools fromhomogenous dynamics and geometry of numbers we prove the existence of acontinuous distribution function $F(r)$ for the normalized deepest cuspexcursions of the unipotent flow. We find closed analytic formulas for $F(r)$for $r \in [-\frac{1}{2} \log 2, \infty)$, and establish asymptotic behavior of$F(r)$ as $r \to -\infty$.

On an extreme value law for the unipotent flow on $\mathrm{SL}_2(\mathbb{R})/\mathrm{SL}_2(\mathbb{Z})$