Year: 2026
Type: preprint
Abstract: We revisit Zhuravlev's 1974 quantitative form of Selberg's sign-change method for the zeros of the Riemann zeta function on the critical line. Zhuravlev's work, originally in Russian and little known in the West, established an explicit positive proportion of such zeros. Using modern techniques we optimise the arithmetic mean value at the heart of the method and obtain the strongest result yet known from Selberg's method, proving that more than $6.78\%$ of the non-trivial zeros of the Riemann zeta function lie on the critical line.
Source: arXiv (Cornell University)
Author: Pearce-Crump, Andrew
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213353958