Nilmoni Karak

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20232026

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math.NT2026

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…

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…