Bulletin of the Australian Mathematical Society· 2026Q2
EXTREME VALUES OF DERIVATIVES OF DIRICHLET L -FUNCTIONS
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- Q2SCImago
- 2026year
Short summary
Derivatives of Dirichlet L-functions can attain extreme values of the same order of magnitude as the original L-functions in the critical strip (1/2 < σ < 1).
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Key points
- Establishes lower bounds for extreme values of Dirichlet L-function derivatives.
- Focuses on the critical strip where 1/2 < σ < 1.
- Shows derivatives can attain extreme values of the same order of magnitude as original L-functions.
- Extends and refines previous work by Aistleitner et al.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract In this paper, we establish lower bounds for extreme values of derivatives of Dirichlet L -functions in the range 1 / 2 < σ < 1 $1/2<\sigma <1$ 1 divided by 2 less than sigma less than 1 . Compared with the work of Aistleitner et al. [‘On large values of L ( σ , χ ) $L(\sigma , \chi )$ upper L left parenthesis sigma comma chi right parenthesis ’, Q. J. Math. 70 (2019), 831–848], our result shows that derivatives of Dirichlet L -functions can attain extreme values of the same order of magnitude as the original L -functions in the interval 1 / 2 < σ < 1 ${1/2<\sigma <1}$ 1 divided by 2 less than sigma less than 1 .
The authors' abstract, as published at the source. Bulletin of the Australian Mathematical Society, 2026 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics