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

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
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preprint

Extreme values of derivatives of Dedekind zeta functions on the $1$-line

Zikang Dong, Qiyu Yang, Shengbo Zhao, Guang-Liang Zhou
arXiv (Cornell University)
Analytic Number Theory Research
preprint

Extreme values of derivatives of Dedekind zeta functions on the $1$-line

Zikang Dong, Qiyu Yang, Shengbo Zhao, Guang-Liang Zhou
preprint en

Abstract

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.

arXiv (Cornell University)
Analytic Number Theory Research
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Extreme values of derivatives of Dedekind zeta functions on the $1$-line — Zikang Dong, Qiyu Yang, et al. · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS