# Elementary Number Theory

By (author)  , Translated by

Free delivery worldwide

Available. Dispatched from the UK in 2 business days
When will my order arrive?

## Description

A translation of Landau's famous Elementare Zahlentheorie with added exercises.

## Product details

• Hardback | 256 pages
• 158.75 x 234.95 x 19.05mm | 521.63g
• Providence, United States
• English
• 0821820044
• 9780821820049
• 816,561

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.