TY  - BOOK
AU  - Halter-Koch,Franz
TI  - Quadratic irrationals: an introduction to classical number theory 
T2  - Pure and applied mathematics. Monographs and textbooks in pure and applied mathematics
SN  - 9781466591837 (hardback)
U1  - 512.74 23
PY  - 2013///
CY  - Boca Raton
PB  - CRC Press
KW  - Quadratic fields
KW  - Algebraic number theory
KW  - MATHEMATICS / Algebra / General
KW  - MATHEMATICS / Number Theory
KW  - MATHEMATICS / Combinatorics
N1  - Includes bibliographical references (p. 407-410) and index; Chapter 1. Quadratic Irrationals 
1.1 Quadratic irrationals, quadratic number fields and discriminants 
1.2 The modular group 
1.3 Reduced quadratic irrationals 
1.4 Two short tables of class numbers  
Chapter 2. Continued Fractions 
2.1 General theory of continued fractions 
2.2 Continued fractions of quadratic irrationals I: General theory 
2.3 Continued fractions of quadratic irrationals II: Special types 
Chapter 3 Quadratic Residues and Gauss Sums 
3.1 Elementary theory of power residues 
3.2 Gauss and Jacobi sums 
3.3 The quadratic reciprocity law 
3.4 Sums of two squares 
3.5 Kronecker and quadratic symbols
Chapter 4. L-Series and Dirichlet's Prime Number Theorem 
4.1 Preliminaries and some elementary cases 
4.2 Multiplicative functions 
4.3 Dirichlet L-functions and proof of Dirichlet's theorem 
4.4 Summation of L-series 
Chapter 5. Quadratic Orders 
5.1 Lattices and orders in quadratic number fields 
5.2 Units in quadratic orders 
5.3 Lattices and (invertible) fractional ideals in quadratic orders 5.4 Structure of ideals in quadratic orders 
5.5 Class groups and class semigroups 
5.6 Ambiguous ideals and ideal classes 
5.7 An application: Some binary Diophantine equations 
5.8 Prime ideals and multiplicative ideal theory 
5.9 Class groups of quadratic orders 
Chapter 6. Binary Quadratic Forms 
6.1 Elementary definitions and equivalence relations 
6.2 Representation of integers 
6.3 Reduction 
6.4 Composition 
6.5 Theory of genera 
6.6 Ternary quadratic forms 
6.7 Sums of squares 
Chapter 7. Cubic and biquadratic residues 
7.1 The cubic Jacobi symbol 
7.2 The cubic reciprocity law 
7.3 The biquadratic Jacobi symbol 
7.4 The biquadratic reciprocity law 
7.5 Rational biquadratic reciprocity laws 
7.6 A biquadratic class group character and applications 
Chapter 8. Class Groups 
8.1 The analytic class number formula 
8.2 L-functions of quadratic orders 
8.3 Ambiguous classes and classes of order divisibility by 4
8.4 Discriminants with cyclic 2-class group: Divisibility by 8 and 16 
Appendix A: Review of Elementary Algebra and Number Theory Appendix B: Some Results from Analysis 
Bibliography 
List of Symbols 
Subject Index
N2  - "This work focuses on the number theory of quadratic irrationalities in various forms, including continued fractions, orders in quadratic number fields, and binary quadratic forms. It presents classical results obtained by the famous number theorists Gauss, Legendre, Lagrange, and Dirichlet. Collecting information previously scattered in the literature, the book covers the classical theory of continued fractions, quadratic orders, binary quadratic forms, and class groups based on the concept of a quadratic irrational"--
ER  -