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 |
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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 |