# Zeta Zeros in a Narrow Vertical Box

Source: [Zeta Zeros in a Narrow Vertical Box](<https://www.sota2.com/research/paper/69cb553f0636e5bf4afca144>)

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

Data updated: 2026-04-01T05:00:12.613Z

Authors: Daniel A. Goldston, Ade Irma Suriajaya

Published: 2026-03-30T07:08:00.000Z

## Abstract

In 1973 Montgomery proved, assuming the Riemann Hypothesis (RH), that asymptotically at least 2/3 of zeros of the Riemann zeta-function are simple zeros. In a previous note (arXiv:2511.20059 \[math.NT\]) we showed how RH can be replaced with a general estimate for a double sum over zeros, and this allows one to then obtain results on zeros that are both simple and on the critical line. Here we give a simple proof based on a direct generalization of Montgomery's proof that on assuming all the zeros are in a narrow vertical box between height $T$ and $2T$ of width $b/\\log T$ and centered on the critical line, then, if $b=b(T)\\to 0$ as $T\\to \\infty$, we have asymptotically at least 2/3 of the zeros are simple and on the critical line.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2603.28104>)

[PDF](<https://arxiv.org/pdf/2603.28104.pdf>)