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arXiv · 2506.22587

The Piltz divisor Problem in Number Fields Using The Resonance Method

Nilmoni Karak·Kamalakshya Mahatab
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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 $Ω-$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.

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Nilmoni Karak, Kamalakshya Mahatab. 2025-06-27. The Piltz divisor Problem in Number Fields Using The Resonance Method. https://arxiv.org/abs/2506.22587

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