2005/09/14 by Kuok Fai Chao, Chao, Kuok Fai, Roger Plymen +1
Engineering · Mathematics · #11M26 #11N05 #11Y35 #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #graph theory and CDMA systems #math.NT #msc:11M26 #msc:11N05 #msc:11Y35
paper · pdf · doi:10.48550/arxiv.math/0509312
Final version, to be published in the International Journal of Number Theory [copyright World Scientific Publishing Company][www.worldscinet.com/ijnt]
openalex publication_date 2005/09/14 · arxiv created 2009/03/23 · arxiv updated 2009/12/01 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
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 × 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.