Zeta Zeros on the Critical Line

Daniel A. Goldston; Ade Irma Suriajaya

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arXiv · 2511.20059

Zeta Zeros on the Critical Line

Daniel A. Goldston·Ade Irma Suriajaya

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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.

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Daniel A. Goldston, Ade Irma Suriajaya. 2025-11-25. Zeta Zeros on the Critical Line. https://arxiv.org/abs/2511.20059

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