> (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?
