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math.RT2025
Borel--Serre type bordifications and Canonical Pairs for Loop groups
Manish M. Patnaik, Punya Plaban Satpathy
To the symmetric space of the (positive half) of a real loop group, we attach a Borel--Serre type bordification and equip it with a Hausdorff topology. The attached boundary, index…
math.NT2025
Erdős-Kac type theorem for the number of scattering geodesics on modular surface
Sudhir Pujahari, Punya Plaban Satpathy
In 1917, Hardy and Ramanujan showed that if is the number of distinct prime factors of a randomly chosen positive integer then the normal order of is $\log \log…
math.NT2025
Prime scattering geodesic theorem
Sudhir Pujahari, Punya Plaban Satpathy
The modular surface, given by the quotient $\mathcal{M} = \Ha/\text{PSL}(2,\Z)$, can be partitioned into a compact subset $\Mm$ and an open neighborhood of the unique cusp in $\mat…