# Zeta Zeros on the Critical Line

Source: [Zeta Zeros on the Critical Line](<https://www.sota2.com/research/paper/69268995d6b0dd3342930408>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-02-07T05:00:14.331Z

Authors: Daniel A. Goldston, Ade Irma Suriajaya

Published: 2025-11-25T08:30:14.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2511.20059>)

[PDF](<https://arxiv.org/pdf/2511.20059.pdf>)