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 condition 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 (Invent Math 86:563–576, 1986) conditional result. This improves upon the work of Wu and Zhao (Mathematika 65:851–861, 2019), who had a similar result.
