The Prime Number Theorem and Pair Correlation of Zeros of the Riemann Zeta-Function
We prove that the error in the prime number theorem can be quantitatively improved beyond the Riemann Hypothesis bound by using versions of Montgomery's conjecture for the pair correlation of zeros of the Riemann zeta-function which are uniform in long ranges and with suitable error terms.
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| Vydáno v: | arXiv.org |
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| Hlavní autoři: | , |
| Médium: | Paper |
| Jazyk: | angličtina |
| Vydáno: |
Ithaca
Cornell University Library, arXiv.org
20.12.2022
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| Témata: | |
| ISSN: | 2331-8422 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | We prove that the error in the prime number theorem can be quantitatively improved beyond the Riemann Hypothesis bound by using versions of Montgomery's conjecture for the pair correlation of zeros of the Riemann zeta-function which are uniform in long ranges and with suitable error terms. |
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| Bibliografie: | SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50 |
| ISSN: | 2331-8422 |
| DOI: | 10.48550/arxiv.2205.06503 |