arXiv subjects
Publications and source records attributed to M. M. Radhika.
We determine the existence of cocompact lattices in groups of the form $\V\rtimes\SL_2(\R)$, where $\V$ is a finite dimensional real representation of $\SL_2(\R)$. It turns out that the answer depends on the parity of $\dim(\V)$ when the representation is irreducible.
We use Morris' theory of Eisenstein series for reductive groups over global function fields in order to extend Harder's computation of Tamagawa numbers to quasi-split groups.
We extend the notion of singular vectors in the context of Diophantine approximation of real numbers with elements of a totally real number field $K$. For $m\geq1$, we establish a version of Dani's correspondence in number fields and prove that under a class of `friendly measures' in $K_S^m$, the set of singular vectors has measure zero. Here $S$ is the set of Archimedean valuations of $K$ and $K_S$ is the product of the completions of $σ(K)$, $σ\in S$. On the other hand, we show the existence of uncountably many non-trivial singular vectors on suitable submanifolds of $K^m_S$ under the action of a certain one parameter subgroup of $\mathrm{SL}_{m+1}(K_S)$.