Year: 2026
Type: preprint
Abstract: We improve our earlier omega bounds for the error term in the Piltz divisor problem over number fields. Our proof uses a weighted extension of a counting theorem of Balasubramanian and Ramachandra and an extension of Lamzouri's kernel to apply the long resonance method. We also discuss applications of our results to lattice points in norm-form regions, invariant sublattices, abelian covers of curves, spectral counting, and representation growth of Heisenberg groups.
Source: arXiv (Cornell University)
Authors: Karak, Nilmoni, Mahatab, Kamalakshya
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214738252