Abstract
Abstract
In this paper, we develop a novel analytic method to prove the prime number theorem in de la Vallée Poussin’s form:
π
(
x
)
=
li
(
x
)
+
O
(
x
e
−
c
log
x
)
. Instead of performing asymptotic expansion on Chebyshev functions as in conventional analytic methods, this new approach uses contour-integration method to analyze Riemann’s prime counting function J(x), which only differs from π(x) by
O
(
x
log
log
x
/
log
x
)
.
Subject
General Physics and Astronomy
Reference14 articles.
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2. Simple Analytic Proof of the Prime Number Theorem;Newman;The American Mathematical Monthly,1980