Unconditional Bounds for Two, Three and Four Consecutive Moderate Gaps between Zeros of the Riemann Zeta Function

Source abstract

We prove unconditional positive-proportion results for consecutive moderate gaps between zeros of the Riemann zeta function. More precisely, for every fixed $0 0$. The proof combines Lamzouri's Hilbert-space formulation of the Montgomery--Taylor second-moment method with local spectral estimates for simple critical-line zeros and a cluster-counting argument that accounts for multiple zeros and zeros off the critical line.