Quadratic irrationals an introduction to classical number theory

Description

Quadratic Irrationals Quadratic irrationals, quadratic number fields and discriminants The modular group Reduced quadratic irrationals Two short tables of class numbers Continued Fractions General theory of continued fractionsContinued fractions of quadratic irrationals I: General theory Continued fractions of quadratic irrationals II: Special types Quadratic Residues and Gauss Sums Elementary theory of power residues Gauss and Jacobi sums The quadratic reciprocity law Sums of two squares Kronecker and quadratic symbols L-Series and Dirichlet's Prime Number Theorem Preliminaries and some elementary cases Multiplicative functions Dirichlet L-functions and proof of Dirichlet's theorem Summation of L-series Quadratic Orders Lattices and orders in quadratic number fields Units in quadratic orders Lattices and (invertible) fractional ideals in quadratic orders Structure of ideals in quadratic orders Class groups and class semigroups Ambiguous ideals and ideal classes An application: Some binary Diophantine equations Prime ideals and multiplicative ideal theory Class groups of quadratic ordersBinary Quadratic Forms Elementary definitions and equivalence relationsRepresentation of integers ReductionComposition Theory of genera Ternary quadratic forms Sums of squaresCubic and Biquadratic Residues The cubic Jacobi symbol The cubic reciprocity law The biquadratic Jacobi symbol The biquadratic reciprocity law Rational biquadratic reciprocity laws A biquadratic class group character and applicationsClass Groups The analytic class number formula L-functions of quadratic orders Ambiguous classes and classes of order divisibility by 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