Extreme values of derivatives of the Dedekind zeta function of a cyclotomic field
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918288659841024 |
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| author | Li, Zhonghua Song, Yutong Yang, Qiyu Zhao, Shengbo |
| author_facet | Li, Zhonghua Song, Yutong Yang, Qiyu Zhao, Shengbo |
| contents | In this paper, we establish a lower bound for the maximum of derivatives of the Dedekind zeta function of a cyclotomic field on the critical line. Employing a double version convolution formula and combing special GCD sums, our result generalizes the work of Bondarenko et al. in 2023. We also set a lower bound by the resonance method when the real part is near the critical line, both of the above results refine part of Yang's work in 2022. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_12342 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extreme values of derivatives of the Dedekind zeta function of a cyclotomic field Li, Zhonghua Song, Yutong Yang, Qiyu Zhao, Shengbo Number Theory 11M06, 11M26, 11N37 In this paper, we establish a lower bound for the maximum of derivatives of the Dedekind zeta function of a cyclotomic field on the critical line. Employing a double version convolution formula and combing special GCD sums, our result generalizes the work of Bondarenko et al. in 2023. We also set a lower bound by the resonance method when the real part is near the critical line, both of the above results refine part of Yang's work in 2022. |
| title | Extreme values of derivatives of the Dedekind zeta function of a cyclotomic field |
| topic | Number Theory 11M06, 11M26, 11N37 |
| url | https://arxiv.org/abs/2506.12342 |