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Elementary Number Theory
Edmund Landau

AMS Chelsea Publishing
1958; 256 pp; hardcover
Volume: 125
Reprint/Revision History:
reprinted 1966; first AMS printing 1999
ISBN-10: 0-8218-2004-4
ISBN-13: 978-0-8218-2004-9
List Price: US$41
Member Price: US$36.90
Order Code: CHEL/125.H
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This is a translation of Landau's famous Elementare Zahlentheorie with added exercises by Paul T. Bateman and Eugene E. Kohlbecker.

This three-volume classic work is reprinted here as a single volume.


"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
  • Number-theoretic 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
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