English

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 Ω\Omega-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

R2 v1 2026-07-01T03:37:14.155Z