Zeta Zeros on the Critical Line
Number Theory
2026-02-06 v2
Abstract
Montgomery in 1973 introduced the pair correlation method to study the vertical distribution of Riemann zeta-function zeros. This work assumed the Riemann Hypothesis (RH). One striking application was a short proof that at least 2/3 of zeta-zeros are simple zeros, the first result of its type. Over the last 50 years, most work on pair correlation of zeta-zeros has continued to assume RH. Here we show that if RH could be removed from Montgomery's simple zero proof, then this would also give a proof that 2/3 of the zeros are simple and on the critical line. This idea has been applied in several recent papers to obtain other results on the zeros.
Cite
@article{arxiv.2511.20059,
title = {Zeta Zeros on the Critical Line},
author = {Daniel A. Goldston and Ade Irma Suriajaya},
journal= {arXiv preprint arXiv:2511.20059},
year = {2026}
}
Comments
expository note, 9 pages