Question

I just taught last semester a course on analytic number theory for 4th year undergraduate students. That was 2 hours a week during 14 weeks; the students had complex analysis before. I had a chapter on Dirichlet's theorem on primes in arithmetic progressions, a chapter on the prime number theorem (proof with a tauberian theorem), and a chapter on some aspects of Riemann's paper (two proofs of the analytic continuation of $\zeta$, the functional equation, the trivial zeroes, the special values).