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Thursday, April 21, 2016

**Abstract:** Let $K$ be a quadratic number field with discriminant $d$. The Dedekind zeta-funciton attached to $K$ can be expressed by $\zeta_{K}(s)=\zeta(s)L(s,\chi_d)$ for $s\ne1$, where $\zeta(s)$ is the Riemann zeta-function, the character $\chi_d$ is the Kronecker symbol associated to $d$, and $L(s,\chi_d)$ is the corresponding Dirichlet $L$-function. Combining Hall’s Method with the twisted second moment of $\zeta_K(1/2+it)$, we show that there are infinitely many gaps between consecutive zeros of $\zeta_K(1/2+it)$ which are greater than $2.866$ times the average spacing. This is joint work with Hung Bui and Winston Heap.