### Abstract

Gauss proved a reciprocity theorem, showing the number of times a ternary positive definite Z-lattice L primitively represents a positive integer d is equal to the number of times the dual of L primitively represents binary quadratic forms of discriminant d / disc L. In this note we extend this theorem to lattices of arbitrary rank over the ring of integers O of a number field K , equipped with either a positive definite or an indefinite quadratic form.

Translated title of the contribution | On a reciprocity theorem of Ghauss |
---|---|

Original language | English |

Title of host publication | Quadratic Forms--Algebra, Arithmetic, and Geometry |

Editors | Ricardo Baeza, Wai Kiu Chan, Detlev W. Hoffmann, Rainer Schulze-Pillot |

Publisher | American Mathematical Society |

Pages | 391 - 397 |

Number of pages | 7 |

Volume | Contemporary Mathematics 493 |

ISBN (Print) | 9780821846483 |

Publication status | Published - 2009 |

## Fingerprint Dive into the research topics of 'On a reciprocity theorem of Gauss'. Together they form a unique fingerprint.

## Cite this

Walling, LH. (2009). On a reciprocity theorem of Gauss. In R. Baeza, W. K. Chan, D. W. Hoffmann, & R. Schulze-Pillot (Eds.),

*Quadratic Forms--Algebra, Arithmetic, and Geometry*(Vol. Contemporary Mathematics 493, pp. 391 - 397). American Mathematical Society. http://books.google.co.uk/books/p/ams?q=walling&vid=ISBN9780821846483&ie=UTF-8&oe=UTF-8&redir_esc=y#v=snippet&q=walling&f=false