Omega bound for the Piltz divisor problem

Nilmoni Karak; Kamalakshya Mahatab

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arXiv · 2609.33820

Omega bound for the Piltz divisor problem

Nilmoni Karak·Kamalakshya Mahatab

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Abstract

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 nonnegative multiplicative functions. The counting theorem gives the estimates needed for the divisor coefficients over a number field and allows us to remove the factor involving the third iterated logarithm from the earlier bounds.

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Nilmoni Karak, Kamalakshya Mahatab. 2026-09-27. Omega bound for the Piltz divisor problem. https://arxiv.org/abs/2609.33820

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