Yoshikatsu Yashiro
Published 2013-11-04, updated 2014-07-18Version 4
In 1874, Mertens proved the approximate formula for partial Euler product for Riemann zeta function at $s=1$, which is called Mertens' theorem. In this paper, we generalize Mertens' theorem for Selberg class and show the prime number theorem for Selberg class.
Oscillations of the error term in the prime number theorem
The error term in the prime number theorem
On the properties of generalized harmonic and oscillatory numbers. Simple proof of the Prime Number Theorem
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