Department of Complex Analysis Prime Number Theorem Gamma function Zeta function
Issue Date:
Aug-2005
Publisher:
Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
Series/Report no.:
2005;1
Abstract:
Some historical remarks on the subject are included in the beginning. In Part one a proof of the Prime Number Theorem following Zagier’s exposition [1997] of Neuman proof [1980]and Korevaar [1982] survey paper is given. The difference here are some changes in the proofs of different steps. In Part two the definitions and some properties of Gamma function and Riemann zeta-function are given. A proof that Prime number Theorem implies nonexistence of zeros of the Riemann zeta-function on the line of complex numbers with real part equal to one is given in this section. In the end of each part some valuable results from 1962, 1975 and 2004 included.
