A new bound for the smallest $x$ with $π(x) > li(x)$
| dc.creator | Chao, Kuok Fai | |
| dc.creator | Plymen, Roger | |
| dc.date | 2005-09-14 | |
| dc.date | 2009-03-23 | |
| dc.date.accessioned | 2026-07-07T12:54:54Z | |
| dc.date.available | 2026-07-07T12:54:54Z | |
| dc.description | We reduce the leading term in Lehman's theorem. This improved estimate allows us to refine the main theorem of Bays and Hudson. Entering $2,000,000$ Riemann zeros, we prove that there exists $x$ in the interval $[exp(727.951858), exp(727.952178)]$ for which $π(x)-\li(x) > 3.2 \times 10^{151}$. There are at least $10^{154}$ successive integers $x$ in this interval for which $π(x)>\li(x)$. This interval is strictly a sub-interval of the interval in Bays and Hudson, and is narrower by a factor of about 12. | |
| dc.description | Final version, to be published in the International Journal of Number Theory [copyright World Scientific Publishing Company][www.worldscinet.com/ijnt] | |
| dc.identifier | https://arxiv.org/abs/math/0509312 | |
| dc.identifier | http://arxiv.org/abs/math/0509312 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/224097 | |
| dc.subject | Number Theory | |
| dc.subject | 11N05; 11Y35; 11M26 | |
| dc.title | A new bound for the smallest $x$ with $π(x) > li(x)$ | |
| dc.type | text |