A note on simple zeros related to Dedekind zeta functions

We give a conditional lower bound on the number of non-trivial simple zeros for the Dedekind zeta function ${\zeta }_K(s)$, where $K$ is a quadratic number field. The conditional result is given by assuming a Lindelöf on average (in the $L^6$ sense) for both $\zeta (s)$ and $L(s,\chi )$, which can be seen as a stronger version of Conrey-Gonek-Ghosh’s \cite{c} conditional result. This improves upon the work of Wu and Zhao \cite{Zhao}, who had a similar result.