| List of Symbols | |
| Preface | |
| Introduction | |
| Background from Algebraic Number Theory | |
| Quadratic Fields: Integers and Units | |
| The Arithmetic of Ideals in Quadratic Fields | |
| The Class Group and Class Number | |
| Reduced Ideals | |
| Quadratic Orders | |
| Powerful Numbers: An Application of Real Quadratics | |
| Continued Fractions Applied to Quadratic Fields | |
| Continued Fractions and Real Quadratics: The Infrastructure | |
| The Continued Fraction Analogue for Complex Quadratics | |
| Diophantine Equations and Class Numbers | |
| Class Numbers and Complex Quadratics | |
| Real Quadratics and Diophantine Equations | |
| Reduced Ideals and Diophantine Equations | |
| Class Numbers and Real Quadratics | |
| Halfway to a Solution | |
| Prime-Producing Polynomials | |
| Complex Prime-Producers | |
| Real Prime-Producers | |
| Density of Primes | |
| Class Numbers: Criteria and Bounds | |
| Factoring Rabinowitsch | |
| Class Number One Criteria | |
| Class Number Bounds via the Divisor Function | |
| The GRH: Relevance of the Riemann Hypothesis | |
| Ambiguous Ideals | |
| Ambiguous Cycles in Real Orders: The Palindromic Index | |
| Exponent Two | |
| Influence of the Infrastructure | |
| Quadratic Residue Covers | |
| Consecutive Powers | |
| Algorithms | |
| Computation of the Class Number of a Real Quadratic Field | |
| Cryptology | |
| Implications of Computational Mathematics for the Philosophy of Mathematics | |
| Appendix A: Tables | |
| Table A1: This is a list of all positive fundamental radicands with class number h? = 1 and period length l , of the simple continued fraction expansion of the principal class, less then 24. Table A8 is known to be unconditionally complete whereas Table |
|
| A1 is complete with one GRH-ruled out exception, as are Tables A2-A4, A6-A7 and A9 | |
| Table A2: This is a subset of Table A1 with D ? 1 (mod 8) | |
| Table A3: h? = 2 for fundamental radicands D > 0 with l ? 24 | |
| Table A4: This is a list of all fundamental radicands of ERD-type with class groups of exponent 2, broken down into three parts depending on congruence modulo 4 of the radicand | |
| Table A5: This three-part table is an illustration of a computer run done for the proof of Theorem 6.2.2 | |
| Table A6: This is a list of all fundamental radicands D > 0 of ERD-type having no split primes less than the Minkowski bound | |
| Table A7: This is a complete list of all fundamental radicands D > 0 with n? ? 0 (see Exercise 3.2.11) and associated regulators, such that the class number is 1 | |
| Table A8: This is a list of all fundamental discriminants D ? 1 (mod 8) of ERD-type with class number less than 24, and is known to be unconditionally complete | |
| Table A9: This table lists all fundamental discriminants of ERD-type with class number 2 | |
| Appendix B: Fundamental Units of Real Quadratic Fields | |
| This list is broken up into three parts according to congruence modulo 4 of fundamental radicands less than 2 . 103 | |
| Appendix C: Class Numbers of Real Quadratic Fields | |
| This table is presented in matrix form with each entry describing a specified class number together with the norm of the fundamental unit with radicands less than 104 | |
| Appendix D: Class Numbers of Complex Quadratic Fields (and their class group structure) | |
| This is a table of fundamental radicands D |
