9 papers
Near Isospectrality and Spectral Rigidity for Compact Locally Symmetric Manifolds
Sudhir Pujahari, Punya Plaban Satpathy
The inverse spectral problem asks to what extent the Laplace--Beltrami spectrum determines the geometry of a Riemannian manifold. We study a natural weakening, called \emph{near is…
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…
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…
Distribution of rational points of an algebraic surface over finite fields
Sudhir Pujahari, Neelam Saikia
The number of points on a certain one parameter family of algebraic surface over a finite field $\F_p$ can be expressed as where is a character sum and i…
Distribution of the Hessian values of Gaussian hypergeometric functions
Ken Ono, Sudhir Pujahari, Hasan Saad +1
We consider a special family of Gaussian hypergeometric functions whose entries are cubic and trivial characters over finite fields. The special values of these functions are known…
The bias conjecture for elliptic curves over finite fields and Hurwitz class numbers in arithmetic progressions
Ben Kane, Sudhir Pujahari, Zichen Yang
In this paper, we consider a version of the bias conjecture for second moments in the setting of elliptic curves over finite fields whose trace of Frobenius lies in an arbitrary fi…