21 citations · 68 across the 14 of their papers we have counts for
15 papers
Shifted second moment of the Riemann zeta function and a Fourier type kernel
Parikshit Dutta, Debashis Ghoshal, Krishnan Rajkumar
We compute the second moment of the Riemann zeta function for shifted arguments over a domain that extends the ones in the literature. We use the Riemann-Siegel formula for the err…
Weyl formula and thermodynamics of geometric flow
Parikshit Dutta, Arghya Chattopadhyay
We study the Weyl formula for the asymptotic number of eigenvalues of the Laplace-Beltrami operator with Dirichlet boundary condition on a Riemannian manifold in the context of geo…
A -arton Model for Modular Cusp Forms
Parikshit Dutta, Debashis Ghoshal
We propose to associate to a modular form (an infinite number of) complex valued functions on the -adic numbers for each prime . We elaborate on the correspond…
Phase operator on and the zeroes of Fisher and Riemann
Parikshit Dutta, Debashis Ghoshal
The distribution of the non-trivial zeroes of the Riemann zeta function, according to the Riemann hypothesis, is tantalisingly similar to the zeroes of the partition functions (Fis…
Pseudodifferential Operators on and -Series
Parikshit Dutta, Debashis Ghoshal
We define a family of pseudodifferential operators on the Hilbert space of complex valued square-integrable functions on the -adic number field $\mathbf{Q}_p…
Matrix Model for Riemann Zeta via its Local Factors
Arghya Chattopadhyay, Parikshit Dutta, Suvankar Dutta +1
We propose the construction of an ensemble of unitary random matrices (UMM) for the Riemann zeta function. Our approach to this problem is `-iecemeal', in the sense that we cons…