This book has grown out of a course of lectures I have given at the
Eidgenossische Technische Hochschule, Zurich. Notes of those lectures,
prepared for the most part by assistants, have appeared in German. This
book follows the same general plan as those notes, though in style, and
in text (for instance, Chapters III, V, VIII), and in attention to
detail, it is rather different. Its purpose is to introduce the
non-specialist to some of the fundamental results in the theory of
numbers, to show how analytical methods of proof fit into the theory,
and to prepare the ground for a subsequent inquiry into deeper
questions. It is pub- lished in this series because of the interest
evinced by Professor Beno Eckmann. I have to acknowledge my indebtedness
to Professor Carl Ludwig Siegel, who has read the book, both in
manuscript and in print, and made a number of valuable criticisms and
suggestions. Professor Raghavan Narasimhan has helped me, time and
again, with illuminating comments. Dr. Harold Diamond has read the
proofs, and helped me to remove obscurities. I have to thank them all.
K.C.