On the elementary proof of the prime number theorem with a remainder term

Authors
Lu, WC
Citation
Wc. Lu, On the elementary proof of the prime number theorem with a remainder term, R MT J MATH, 29(3), 1999, pp. 979-1053
Citations number
5
Categorie Soggetti
Mathematics
Journal title
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
ISSN journal
00357596 → ACNP
Volume
29
Issue
3
Year of publication
1999
Pages
979 - 1053
Database
ISI
SICI code
0035-7596(199923)29:3<979:OTEPOT>2.0.ZU;2-Q
Abstract
In this paper we have improve the remainder term of the prime number theore m by using the elementary method, Selberg's method, and obtained pi(x) = li x + O{x exp(-log((1/2)-epsilon) x)}, where epsilon > 0 is an arbitrarily s mall constant, and the O is dependent on epsilon.