Extreme values of derivatives of Dedekind zeta functions on the $1$-line
In this paper, we establish lower bounds for extreme values of derivatives of Dedekind zeta functions on the \(1\)-line over arbitrary fixed number fields. Our result extends Yang's corresponding estimate for the Riemann zeta function in 2024, with the leading constant involving residues of Dedekind zeta functions and a moment of the Dickman function. A key ingredient is a uniform asymptotic formula for weighted friable sums involving the coefficients of Dedekind zeta functions.
Authors
- Zikang Dong (ORCID: https://orcid.org/0000-0002-3868-1361)
- Qiyu Yang (ORCID: https://orcid.org/0000-0001-5700-8685)
- Shengbo Zhao
- Guang-Liang Zhou
Publication Details
- Journal
- arXiv (Cornell University)
- Published
- 2026-11-02
- DOI
- https://doi.org/10.48550/arxiv.2611.02675
- Primary Topic
- Analytic Number Theory Research
- Type
- preprint