Nilmoni Karak

collaborators

4 papers

math.NT2026

Sharp lower bounds for shifted moments of Dedekind zeta functions

Benjamin Durkan, Nilmoni Karak, Kamalakshya Mahatab

Let $K_{1}, \dots, K_{r}$ be fixed number fields, and let $L$ be the compositum of their Galois closures. Assuming GRH for $ζ_{L}$ , we prove a sharp lower bound for products of shifted De…

math.NT2026

Sharp Upper Bounds for Moments of Dedekind Zeta Functions

Benjamin Durkan, Nilmoni Karak, Kamalakshya Mahatab

Assuming the Generalised Riemann Hypothesis, we establish conjecturally sharp upper bounds for shifted moments of products of Dedekind zeta functions of arbitrary number fields. Th…

math.NT2025

Omega Estimate for the Lattice Point Discrepancy of a Body of Revolution Using The Resonance Method

Nilmoni Karak

Using a recent method developed by Mahatab, we obtain an improved $Ω$ -bound for the error term arising in lattice counting problem of bodies of revolution in $R^{3}$ around a…

math.NT2025

The Piltz divisor Problem in Number Fields Using The Resonance Method

Nilmoni Karak, Kamalakshya Mahatab

The Piltz divisor problem is a natural generalization of the classical Dirichlet divisor problem. In this paper, we study this problem over number fields and obtain improved $Ω -$ bo…