| Autor: |
Baluyot, Siegfred Alan C., Goldston, Daniel Alan, Suriajaya, Ade Irma, Turnage-Butterbaugh, Caroline L. |
| Rok vydání: |
2023 |
| Předmět: |
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| Zdroj: |
Acta Arith. 214 (2024), 357-376 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.4064/aa230612-20-3 |
| Popis: |
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 $\rho=\beta+i\gamma$ of the Riemann zeta-function such that $T^{3/8}<\gamma\le T$ satisfy $|\beta-1/2|<1/(2\log T)$, %lie in the thin box $\{s=\sigma +it: |\sigma-1/2|<1/(2\log T),\ T^{3/8}Comment: 13 pages, dedicated to Henryk Iwaniec on the occasion of his 75th birthday |
| Databáze: |
arXiv |
| Externí odkaz: |
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