Pair Correlation Conjecture for the zeros of the Riemann zeta-function II: The Alternative Hypothesis
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916834593210368 |
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| author | Goldston, Daniel A. Lee, Junghun Schettler, Jordan Suriajaya, Ade Irma |
| author_facet | Goldston, Daniel A. Lee, Junghun Schettler, Jordan Suriajaya, Ade Irma |
| contents | In an earlier paper, we proved that Montgomery's Pair Correlation Conjecture (PCC) for zeros of the Riemann zeta-function can be used to prove without the assumption of the Riemann Hypothesis (RH) that asymptotically 100% of the zeros are both simple and on the critical line. This is based on a method of Gallagher and Mueller from 1978. We formulate an appropriate form of the Alternative Hypothesis (AH), which determines a different PCC, and, using the same method as above, prove that asymptotically, 100% of the zeros are both simple and on the critical line. As in our previous paper, we do not assume RH. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06823 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pair Correlation Conjecture for the zeros of the Riemann zeta-function II: The Alternative Hypothesis Goldston, Daniel A. Lee, Junghun Schettler, Jordan Suriajaya, Ade Irma Number Theory 11M06, 11M26 In an earlier paper, we proved that Montgomery's Pair Correlation Conjecture (PCC) for zeros of the Riemann zeta-function can be used to prove without the assumption of the Riemann Hypothesis (RH) that asymptotically 100% of the zeros are both simple and on the critical line. This is based on a method of Gallagher and Mueller from 1978. We formulate an appropriate form of the Alternative Hypothesis (AH), which determines a different PCC, and, using the same method as above, prove that asymptotically, 100% of the zeros are both simple and on the critical line. As in our previous paper, we do not assume RH. |
| title | Pair Correlation Conjecture for the zeros of the Riemann zeta-function II: The Alternative Hypothesis |
| topic | Number Theory 11M06, 11M26 |
| url | https://arxiv.org/abs/2507.06823 |