Our object is to introduce the interested student to the techniques, results, and terminology of multiplicative number theory. It is not intended that our discussion will always reach the research frontier. Rather, it is hoped that the material here will prepare the student for intelligent reading of the more advanced research literature.
Analytic number theorists are not very uniformly distributed around the world and it possible that a student may be working without the guidance of an experienced mentor in the area. With this in mind, we have tried to make this volume as self-contained as possible.
We assume that the reader has some acquaintance with the fundamentals of elementary number theory, abstract algebra, measure theory, complex analysis, and classical harmonic analysis. More specialized or advanced background material in analysis is provided in the appendices.
The relationship of exercises to the material developed in a given section varies widely. Some exercises are designed to illustrate the theory directly whilst others are intended to give some idea of the ways in which the theory can be extended, or developed, or paralleled in other areas. The reader is cautioned that papers cited in exercises do not necessarily contain a solution.
This volume is the first instalment of a larger project.