Gaps between zeros of Dedekind zeta-functions of quadratic number fields

Let K be a quadratic number field, and let ζK(s) denote the Dedekind zeta-function attached to K. Using the mixed second moments of derivatives of ζK(12+it), we prove the existence of gaps between consecutive zeros of ζK(s) on the critical line which are at least 6=2.44949… times the average spacing.