Full Record

Author | Shepherd, Rick L. |

Title | Binary quadratic forms and genus theory |

URL | http://libres.uncg.edu/ir/listing.aspx?styp=ti&id=15057 |

Publication Date | 2013 |

Degree Level | masters |

University/Publisher | University of North Carolina – Greensboro |

Abstract | The study of binary quadratic forms arose as a natural generalization of questions about the integers posed by the ancient Greeks. A major milestone of understanding occurred with the publication of Gauss's <italic>Disquisitiones Arithmeticae</italic> in 1801 in which Gauss systematically treated known results of his predecessors and vastly increased knowledge of this part of number theory. In effect, he showed how collections of sets of binary quadratic forms can be viewed as groups, at a time before group theory formally existed. Beyond that, he even defined and calculated genus groups, which are essentially quotient groups, that explain which congruence classes of numbers can be represented by given sets of forms. This thesis examines Gauss's main results as interpreted and refined over two centuries. Also code has been created to implement many of the algorithms used in studying the relationships of such forms to each other, to generate examples, and to provide a small toolkit of software for analyzing the corresponding algebraic structures.; Binary quadratic forms, Class groups, Class number, Genus theory, PARI code |

Subjects/Keywords | Forms, Binary; Forms, Quadratic; Group theory |

Contributors | Brett Tangedal (advisor) |

Country of Publication | us |

Record ID | oai:nc-docks:15057 |

Repository | nc-docks |

Date Retrieved | 2019-01-23 |

Date Indexed | 2019-01-23 |

Grantor | The University of North Carolina at Greensboro |