Abstract
We prove logarithm laws and shrinking target properties for unipotent flows on the homogenous space Γ\ G with $${G= {\rm SL}_2(\mathbb{R})^{r_1}\times{\rm SL}_2(\mathbb{C})^{r_2}}$$ and $${\Gamma \subseteq G}$$ an irreducible non-uniform lattice. Our method relies on certain estimates for the norms of (incomplete) theta series in this setting.
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