18 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…
A Bombieri-Vinogradov-type theorem for moduli with small radical
Stephan Baier, Sudhir Pujahari
In this article, we extend our recent work on a Bombieri-Vinogradov-type theorem for sparse sets of prime powers with to sparse sets…
Sato-Tate Distribution of -adic hypergeometric functions
Sudhir Pujahari, Neelam Saikia
Recently Ono, Saad and the second author \cite{KHN} initiated a study of value distribution of certain families of Gaussian hypergeometric functions over large finite fields. They…
Turán inequalities for the plane partition function
Ken Ono, Sudhir Pujahari, Larry Rolen
Heim, Neuhauser, and Tröger recently established some inequalities for MacMahon's plane partition function that generalize known results for Euler's partition func…
Odd moments for the trace of Frobenius and the Sato--Tate conjecture in arithmetic progressions
Kathrin Bringmann, Ben Kane, Sudhir Pujahari
In this paper, we consider the moments of the trace of Frobenius of elliptic curves if the trace is restricted to a fixed arithmetic progression. We determine the asymptotic behavi…
Formulas for moments of class numbers in arithmetic progressions
Kathrin Bringmann, Ben Kane, Sudhir Pujahari
In this paper, we obtain explicit formulas for the second moments for Hurwitz class numbers with running through a fixed congruence class modulo .
A Bombieri-Vinogradov-type theorem with prime power moduli
Stephan Baier, Sudhir Pujahari
In 2020, Roger Baker \cite{Bak} proved a result on the exceptional set of moduli in the prime number theorem for arithmetic progressions of the following kind. Let be…
Zeros of higher derivatives of Riemann zeta function
Mithun Kumar Das, Sudhir Pujahari
In this article, we extend the result of Conrey [5, Theorem 2] to shorter intervals for higher-order derivatives of the zeta function. That is we study the mean value of the produc…
Distribution of moments of Hurwitz class numbers in arithmetic progressions and holomorphic projection
Ben Kane, Sudhir Pujahari
In this paper, we study moments of Hurwitz class numbers associated to imaginary quadratic orders restricted into fixed arithmetic progressions. In particular, we fix in an ari…
Distinguishing pure representations by normalized traces
Manish Kumar Pandey, Sudhir Pujahari, Jyoti Prakash Saha
Given two pure representations of the absolute Galois group of an -adic number field with coefficients in (with ), we show that the Frob…
Effective joint distribution of eigenvalues of Hecke operators
Sudhir Pujahari
In 1997, Serre proved that the eigenvalues of normalised -th Hecke operator acting on the space of cusp forms of weight and level are equidistributed in $[-2,2…
Distribution of gaps between eigenangles of Hecke operators
Sudhir Pujahari
In 1931, Van der Corput showed that if for each positive integer , the sequence is uniformly distributed (mod 1), then the sequence is uniformly distribu…
Sign changes of coefficients of certain Dirichlet series
Jaban Meher, Sudhir Pujahari, Karam Deo Shankhadhar
In this paper, we give criteria for infinitely many sign changes of the coefficients of any Dirichlet series if the coefficients are real numbers. We also provide examples where ou…