ON SIMPLE ZEROS OF THE DEDEKIND ZETA‐FUNCTION OF A QUADRATIC NUMBER FIELD

We study the number of non-trivial simple zeros of the Dedekind zeta-function of a quadratic number field in the rectangle . We prove that such a number exceeds if is sufficiently large. This improves upon the classical lower bound established by Conrey et al [Simple zeros of the zeta function of a quadratic number field. I. Invent. Math. 86 (1986), 563–576].