This book was written for graduate students looking for an introduction to
some basic methods of analytic number theory. It is suitable as a textbook
for an introductory one-semester course at the beginning graduate level, but
contains more material than can be comfortably covered in such a course.
However, by suitably selecting chapters, it is possible to teach courses going
in various directions.
Readers should be familiar with ε-δ calculus, have completed an under-
graduate course in complex analysis, and possess the proficiency in abstract
and linear algebra to be expected of a beginning graduate student. No
familiarity with graduate-level analysis is assumed. The first four chapters
presuppose no complex analysis beyond simple properties of the exponential
Each chapter is followed by notes with references and historical remarks.
At the end of many of the sections there are references to more detailed
treatments of the topic under consideration.
I wish to thank anonymous referees for suggestions that have improved
the book. Naturally I alone remain responsible for all errors and imperfec-
tions that remain.
This seems an appropriate place to express my gratitude to Hugh Mont-
gomery, Imre Ruzsa, and the late Sigmund Selberg, from whose teaching of
analytic number theory I have benefited.