This book shows the scope of analytic number theory both in classical and
modern directions. There are no division lines; in fact our intent is to demonstrate,
particularly for newcomers, the fascinating countless interrelations. Of course, our
picture of analytic number theory is by no means complete, but we tried to frame
the material into a portrait of a reasonable size, yet providing a self-contained
presentation.
We were writing this book in a period of time during and after teaching courses
and working with graduate students in Rutgers University, Bordeaux University and
Courant Institute. We thank these institutions for providing conditions for both
of us to work together. We shared ideas on what this book should be about with
many of our colleagues, who gave us critical suggestions. Among them we would like
to mention Etienne Fouvry, John Friedlander, Philippe Michel and Peter Sarnak.
During a long process of typing and preparation of this book for publication, we
received stimulating encouragement and technical advice from Sergei Gelfand, for
all of his help we express our gratitude. Carol Hamer helped to polish some of our
English phrases while her little boys tried to destroy the TeX files without success.
We thank them all for the output.