Year: 2026
Type: preprint
Abstract: For every fixed primitive Dirichlet $L$-function and every $\varepsilon>0$, we prove unconditionally that infinitely many consecutive zeros have spacing less than $1/2+\varepsilon$ times the mean. Assuming the Riemann Hypothesis, we also prove a positive proportion of such spacings for the Riemann zeta-function, and infinitely many spacings greater than $3.63$ times the mean for every fixed primitive Dirichlet $L$-function.
Source: arXiv (Cornell University)
Authors: Durkan, Benjamin, Pearce-Crump, Andrew
Institutions: University of Manchester, University of Bristol
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223105786