Complex analysis - sci.math

Message from discussion Complex analysis

kleptomaniac6...@hotmail.com

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More options Jul 24, 7:01 am

Newsgroups: sci.math

From: kleptomaniac6...@hotmail.com

Date: Wed, 23 Jul 2008 16:01:28 -0700 (PDT)

Local: Thurs, Jul 24 2008 7:01 am

Subject: Complex analysis

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(1) Does anyone have any recommendations for a good textbook on
complex analysis? The background intention is to study the Riemann
Zeta function and the distribution of primes, complex analytic proof
of the prime number theorem, and related results - preferably no
functional analysis, advanced topology, open covers etc.

(2) A certain statement in analytic number theory is the following:
psi(a,b,x) = (1/phi(b))x + O(sqrt(x)log^2(x)), where psi(a,b,x) sums
the logarithm of the relevant prime for each power of a prime less
than x, where the prime is congruent to a modulo b. Is this equivalent
to, or a consequence of, the Riemann hypothesis, or the Generalized
Riemann Hypothesis?

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