Year: 2026
Type: preprint
Abstract: We provide explicit bounds on the number of zeros for $ζ$ in short intervals near the edge of the critical strip. Ultimately we show that even in short intervals a positive proportion of zeros will not be near the edge of the critical strip. For example with $h>100$ and $t>10^{100}$ the proportion of zeros of $ζ$ with imaginary part in $[t-h,t+h]$ which have real part in $[\frac{1}{16},\frac{15}{16}]$ is at least $13\%$ and a positive proportion is already obtained at $t>10^{43}$.
Source: arXiv (Cornell University)
Author: Fiori, Andrew
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214030784