6 papers
Omega bound for the Piltz divisor problem
Nilmoni Karak, Kamalakshya Mahatab
We obtain improved omega bounds for the error term in the Piltz divisor problem over number fields. Our proof combines Lamzouri's resonance argument with a counting theorem for non…
Sharp lower bounds for shifted moments of Dedekind zeta functions
Benjamin Durkan, Nilmoni Karak, Kamalakshya Mahatab
Let be fixed number fields, and let be the compositum of their Galois closures. Assuming GRH for , we prove a sharp lower bound for products of shifted De…
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…
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 -bound for the error term arising in lattice counting problem of bodies of revolution in around a…
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 bo…
A Dirichlet character analogue of Ramanujan's formula for odd zeta values
Anushree Gupta, Md Kashif Jamal, Nilmoni Karak +1
In 2001, Kanemitsu, Tanigawa, and Yoshimoto studied the following generalized Lambert series, for and…