EXTREME VALUES OF DERIVATIVES OF THE DEDEKIND ZETA FUNCTION OF A CYCLOTOMIC FIELD
Abstract
Abstract In this paper, we establish a lower bound for the maxima of derivatives of the Dedekind zeta function of a cyclotomic field on the critical line. Employing a double-version convolution formula and combined with special GCD sums, our result generalizes the work of Bondarenko et al . [‘A dichotomy for extreme values of zeta and Dirichlet L-functions’, Bull. Lond. Math. Soc. 55 (2023), 2963–2975]. We also establish a lower bound via the resonance method when the real part is near the critical line; both of the above results refine parts of Yang’s [‘Extreme values of derivatives of the Riemann zeta function’, Mathematika 68 (2022), 486–510] work.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Analytic Number Theory Research
Meromorphic and Entire Functions
Publication details
- Journal / source
- Journal of the Australian Mathematical Society
- Publisher
- Cambridge University Press (CUP)
- Pages
- 1–27
- Publication date
- 16 June 2026
- Language
- EN