English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We settle a conjecture of Farmer and Ki in a stronger form. Roughly speakingwe show that there is a positive proportion of small gaps between consecutivezeros of the zeta-function $\zeta(s)$ if and only if there is a positiveproportion of zeros of $\zeta'(s)$ lying very closely to the half-line. Ourwork has applications to the Siegel zero problem. We provide a criterion forthe non-existence of the Siegel zero, solely in terms of the distribution ofthe zeros of $\zeta(s)$. Finally on the Riemann Hypothesis and the PairCorrelation Conjecture we obtain near optimal bounds for the number of zeros of$\zeta'(s)$ lying very closely to the half-line. Such bounds are relevant to adeeper understanding of Levinson's method, allowing us to place one-third ofthe zeros of the Riemann zeta-function on the half-line.

Gaps between zeros of $\zeta(s)$ and the distribution of zeros of $\zeta'(s)$