Gaps between zeros of Dedekind zeta-functions of quadratic number fields. II (Q2833460)

Let \(\zeta_K(s)\) be the Dedekind zeta-function of a quadratic field \(K\) of discriminant \(D\) and let \(t_n+\frac{1}{2}i\) be the sequence of its zeros lying in the upper half-plane on the critical line. It is conjectured that NEWLINE\[NEWLINE\Lambda_K:=\limsup_{n\to\infty}{1\over\pi}(t_{n+1}-t_n)\bigl(\log(|D|^{1/2}t_n\bigr)=\infty,NEWLINE\]NEWLINE and the third author showed that \(\Lambda_K>2.449\) [\textit{C. L. Turnage-Butterbaugh}, J. Math. Anal. Appl. 418, No. 1, 100--107 (2014; Zbl 1306.11091)], using results of [\textit{W. Heap}, Int. J. Number Theory 10, No. 1, 235--281 (2014; Zbl 1314.11054)] on twisted moments of \(\zeta_K(s)\). In this paper, the authors obtain \(\Lambda_K>2.866\) using a similar approach and utilizing an improvement of Heap's result obtained recently by \textit{S. Mettin} et al. [``A quadratic divisor problem and moments of the Riemann zeta-function'', Preprint, \url{arXiv:1609.02539}].