Elementary Number Theory
American Mathematical Society (Verlag)
978-0-8218-2004-9 (ISBN)
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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.
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.
| Erscheint lt. Verlag | 30.8.1999 |
|---|---|
| Reihe/Serie | AMS Chelsea Publishing |
| Verlagsort | Providence |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
| ISBN-10 | 0-8218-2004-4 / 0821820044 |
| ISBN-13 | 978-0-8218-2004-9 / 9780821820049 |
| Zustand | Neuware |
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