Introduction to Analytic Number Theory

✍ Scribed by Prof. Dr. K. Chandrasekharan (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1968
• Tongue: English
• Leaves: 150
• Series: Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete 148
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages I-VIII
The unique factorization theorem....Pages 1-10
Congruences....Pages 11-17
Rational approximation of irrationals and Hurwitz’s theorem....Pages 18-25
Quadratic residues and the representation of a number as a sum of four squares....Pages 26-33
The law of quadratic reciprocity....Pages 34-44
Arithmetical functions and lattice points....Pages 45-62
Chebyshev’s theorem on the distribution of prime numbers....Pages 63-83
Weyl’s theorems on uniform distribution and Kronecker’s theorem....Pages 84-96
Minkowski’s theorem on lattice points in convex sets....Pages 97-104
Dirichlet’s theorem on primes in an arithmetical progression....Pages 105-121
The prime number theorem....Pages 122-130
Back Matter....Pages 131-143

✦ Subjects

Mathematics, general