Hello all --
I have the privilege of teaching an introductory graduate course in analytic number theory at the University of South Carolina this fall. What topics should I definitely cover?
I'm not lacking for good material of course. I intend to cover much of Davenport; there is also Cojocaru and Murty's introduction to sieve methods; there is interesting elementary work by Chebyshev et al. on counting primes; there is also Apostol's excellent book; I could dip into Pollack's new book; and there are many other excellent sources as well. I should also make sure the students master partial summation, big-O, and the kinds of contour integration that come up in typical problems.
I feel prepared to do a good job, and I will also have good people to ask for advice in my new department, but I would cheerfully welcome further advice, opinions, etc. from anyone who would like to offer them. Any thoughts?
Thanks to all. --Frank