Abstract
We prove logarithm laws and shrinking target properties for unipotent flows on the homogenous space $Γ\bs G$ with $G=\SL_2(\bbR)^{r_1}\times\SL_2(\bbC)^{r_2}$ and 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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