Extreme Values of Derivatives of Dirichlet L -Functions

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<σ <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(σ , χ ) 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<σ <1 1 divided by 2 less than sigma less than 1 .