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- W4380136175 abstract "Assuming the Riemann Hypothesis (RH), Montgomery proved a theorem concerning pair correlation of zeros of the Riemann zeta-function. One consequence of this theorem is that, assuming RH, at least $67.9%$ of the nontrivial zeros are simple. Here we obtain an unconditional form of Montgomery's theorem and show how to apply it to prove the following result on simple zeros: Assuming all the zeros $rho=beta+igamma$ of the Riemann zeta-function such that $T^{3/8}<gammale T$ satisfy $|beta-1/2|<1/(2log T)$, %lie in the thin box ${s=sigma +it: |sigma-1/2|<1/(2log T), T^{3/8}<tle T}$, then, as $T$ tends to infinity, at least $61.7%$ of these zeros are simple. The method of proof neither requires nor provides any information on whether any of these zeros are on or not on the critical line where $beta=1/2$. We also obtain the same result under the weaker assumption of a strong zero-density hypothesis." @default.
- W4380136175 created "2023-06-10" @default.
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- W4380136175 date "2023-06-07" @default.
- W4380136175 modified "2023-09-27" @default.
- W4380136175 title "An unconditional Montgomery Theorem for Pair Correlation of Zeros of the Riemann Zeta Function" @default.
- W4380136175 doi "https://doi.org/10.48550/arxiv.2306.04799" @default.
- W4380136175 hasPublicationYear "2023" @default.
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