Topics in Multiplicative Number Theory

Three basic principles.- The large sieve.- Arithmetic formulations of the large sieve.- A weighted sieve and its application.- A lower bound of Roth.- Classical mean value theorems.- New mean value theorems.- Large moduli theorems.- Further results and conjectures concerning mean and large moduli.- Mean moduli of L-functions.- Zero-free regions and the proliferation of zeros.- Distribution of zeros of L-functions.- Least character non-residues and arg L(12+it, x).- The prime number theorems of Hoheisel and Selberg.- The bombieri — Vinogradov theorem.- A lemma in additive prime number theory.- The mean value theorem of Barban.