Extreme values of derivatives of Dedekind zeta functions on the 1-line
Zikang Dong, Qiyu Yang, Shengbo Zhao, Guang-Liang Zhou
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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