The Piltz divisor Problem in Number Fields Using The Resonance Method
Number Theory
2025-07-01 v1
Abstract
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 bounds for its error terms. Our approach involves generalizing a Voronoi-type formula due to Soundararajan in the number field setting, and applying a recent result due to the second author.
Cite
@article{arxiv.2506.22587,
title = {The Piltz divisor Problem in Number Fields Using The Resonance Method},
author = {Nilmoni Karak and Kamalakshya Mahatab},
journal= {arXiv preprint arXiv:2506.22587},
year = {2025}
}
Comments
11 pages