The Piltz divisor Problem in Number Fields Using The Resonance Method
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916814390296576 |
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| author | Karak, Nilmoni Mahatab, Kamalakshya |
| author_facet | Karak, Nilmoni Mahatab, Kamalakshya |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22587 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Piltz divisor Problem in Number Fields Using The Resonance Method Karak, Nilmoni Mahatab, Kamalakshya Number Theory 11R42, 11P21, 11N37 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. |
| title | The Piltz divisor Problem in Number Fields Using The Resonance Method |
| topic | Number Theory 11R42, 11P21, 11N37 |
| url | https://arxiv.org/abs/2506.22587 |