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

TL;DR

This paper proves that for quadratic number fields, there are infinitely many large gaps between zeros of their Dedekind zeta-functions, exceeding 2.866 times the average spacing, highlighting significant irregularities in zero distribution.

Contribution

It establishes the existence of infinitely many large gaps between zeros of Dedekind zeta-functions of quadratic fields, quantifying the minimal size of these gaps.

Findings

Infinitely many gaps exceed 2.866 times the average spacing.

Large gaps are proven to occur infinitely often on the critical line.

Quantitative bound on the size of gaps between zeros.

Abstract

Let $K$ be a quadratic number field and $\zeta_K(s)$ be the associated Dedekind zeta-function. We show that there are infinitely many normalized gaps between consecutive zeros of $\zeta_K(s)$ on the critical line which are greater than $2.866$ times the average spacing.