A new bound for the smallest x with π(x) > li(x)
Chao, Kuok Fai and Plymen, Roger (2010) A new bound for the smallest x with π(x) > li(x). International Journal of Number Theory, 6, (3), 681-690. (doi:10.1142/S1793042110003125)
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Description/Abstract
We reduce the leading term in Lehman's theorem. This improved estimate allows us to refine the main theorem of Bays and Hudson [2]. 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 × 10151. There are at least 10154 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.
| Item Type: | Article |
|---|---|
| ISSN: | 1793-0421 (print) 1793-7310 (electronic) |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | University Structure - Pre August 2011 > School of Mathematics > Pure Mathematics |
| ePrint ID: | 173715 |
| Deposited On: | 09 Mar 2011 15:09 |
| Last Modified: | 02 Mar 2012 13:59 |
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