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PreprintCC0arXiv

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

  • Zikang Dong
  • Qiyu Yang
  • Shengbo Zhao
  • Guang-Liang Zhou
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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.

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Cite

BibTeXRIS
BibTeX
@misc{dong2026extreme,
  title = {{Extreme values of derivatives of Dedekind zeta functions on the $1$-line}},
  author = {Zikang Dong and Qiyu Yang and Shengbo Zhao and Guang-Liang Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.02675},
  eprint = {2611.02675},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.02675},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Extreme values of derivatives of Dedekind zeta functions on the $1$-line
AU  - Zikang Dong
AU  - Qiyu Yang
AU  - Shengbo Zhao
AU  - Guang-Liang Zhou
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.02675
UR  - https://arxiv.org/abs/2611.02675
AB  - 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.
ER  -