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By employing the assessment of the asymptotic size of various sums of G\'{a}lstudied by La Bret\`eche and Tenenbaum, we provide an improvement on the recentresult of A. Bondarenko, P. Darbar, M. V. Hagen, W. Heap, and K. Seip regardingthe large values of the Dedekind zeta-function on the critical line.Specifically, let $d\geqslant 3$ be an integer and $A$ be a positive constant.Denoting $K=\mathbb{Q}(\zeta_d)$, we establish that, if $T$ is sufficientlylarge, then uniformly for $d \ll (\log\log T)^A$, \begin{equation*} \max_{ t\in [0,T]}\left|\zeta_K \left(\frac{1}{2}+it \right) \right| \gg\exp\left({(1+o(1))\varphi(d)} \sqrt{\frac{\log T \log \log \log T}{\log \logT}} \right). \end{equation*}

Extreme values of the Dedekind zeta function on the critical line