AMS Chelsea Publishing 1958; 256 pp; hardcover Volume: 125 Reprint/Revision History: reprinted 1966; first AMS printing 1999 ISBN10: 0821820044 ISBN13: 9780821820049 List Price: US$41 Member Price: US$36.90 Order Code: CHEL/125.H
 This is a translation of Landau's famous Elementare Zahlentheorie with added exercises by Paul T. Bateman and Eugene E. Kohlbecker. This threevolume classic work is reprinted here as a single volume. Reviews "These three excellently printed and arranged volumes form an addition of the highest importance to the literature of the theory of numbers. With them, the reader familiar with the basic elements of the theory of functions of a real and complex variable, can follow many of the astonishing recent advances in this fascinating field. His interest is enlisted at once and sustained by the accuracy, skill, and enthusiasm with which Landau marshals the analytic facts and simplifies as far as possible the inevitable mass of details ... "The mathematical world owes a great debt of gratitude to Professor Landau for rendering accessible so many of the recent splendid achievements in the theory of numbers."  G. D. Birkhoff, Bulletin of the AMS Table of Contents Part One. Foundations of Number Theory  The greatest common divisor of two numbers
 Prime numbers and factorization into prime factors
 The greatest common divisor of several numbers
 Numbertheoretic functions
 Congruences
 Quadratic residues
 Pell's equation
Part Two. Brun's Theorem and Dirichlet's Theorem  Introduction
 Some elementary inequalities of prime number theory
 Brun's theorem on prime pairs
 Dirichlet's theorem on the prime numbers in an arithmetic progression; Further theorems on congruences; Characters; \(L\)series; Dirichlet's proof
Part Three. Decomposition into Two, Three, and Four Squares  Introduction
 Farey fractions
 Decomposition into two squares
 Decomposition into four squares; Introduction; Lagrange's theorem; Determination of the number of solutions
 Decomposition into three squares; Equivalence of quadratic forms; A necessary condition for decomposability into three squares; The necessary condition is sufficient
Part Four. The Class Number of Binary Quadratic Forms  Introduction
 Factorable and unfactorable forms
 Classes of forms
 The finiteness of the class number
 Primary representations by forms
 The representation of \(h(d)\) in terms of \(K(d)\)
 Gaussian sums; Appendix; Introduction; Kronecker's proof; Schur's proof; Mertens' proof
 Reduction to fundamental discriminants
 The determination of \(K(d)\) for fundamental discriminants
 Final formulas for the class number
Appendix. Exercises  Exercises for part one
 Exercises for part two
 Exercises for part three
 Index of conventions; Index of definitions
 Index
