Author | Buell, Duncan A. author |
---|---|
Title | Binary Quadratic Forms [electronic resource] : Classical Theory and Modern Computations / by Duncan A. Buell |
Imprint | New York, NY : Springer New York, 1989 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4542-1 |
Descript | X, 248 p. online resource |
1 Elementary Concepts -- 2 Reduction of Positive Definite Forms -- 3 Indefinite Forms -- 3.1 Reduction, Cycles -- 3.2 Automorphs, Pellโs Equation -- 3.3 Continued Fractions and Indefinite Forms -- 4 The Class Group -- 4.1 Representation and Genera -- 4.2 Composition Algorithms -- 4.3 Generic Characters Revisited -- 4.4 Representation of Integers -- 5 Miscellaneous Facts -- 5.1 Class Number Computations -- 5.2 Extreme Cases and Asymptotic Results -- 6 Quadratic Number Fields -- 6.1 Basic Algebraic Definitions -- 6.2 Algebraic Numbers and Quadratic Fields -- 6.3 Ideals in Quadratic Fields -- 6.4 Binary Quadratic Forms and Classes of Ideals -- 6.5 History -- 7 Composition of Forms -- 7.1 Nonfundamental Discriminants -- 7.2 The General Problem of Composition -- 7.3 Composition in Different Orders -- 8 Miscellaneous Facts II -- 8.1 The Cohen-Lenstra Heuristics -- 8.2 Decomposing Class Groups -- 8.3 Specifying Subgroups of Class Groups -- 9 The 2-Sylow Subgroup -- 9.1 Classical Results on the Pell Equation -- 9.2 Modern Results -- 9.3 Reciprocity Laws -- 9.4 Special References for Chapter 9 -- 10 Factoring with Binary Quadratic Forms -- 10.1 Classical Methods -- 10.2 SQUFOF -- 10.3 CLASNO -- 10.4 SPAR -- 10.5 CFRAC -- 10.6 A General Analysis -- Appendix 1:Tables, Negative Discriminants -- Appendix 2:Tables, Positive Discriminants