On a reciprocity theorem of Gauss

Research output: Chapter in Book/Report/Conference proceedingChapter in a book

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 contributionOn a reciprocity theorem of Ghauss
Original languageEnglish
Title of host publicationQuadratic Forms--Algebra, Arithmetic, and Geometry
EditorsRicardo Baeza, Wai Kiu Chan, Detlev W. Hoffmann, Rainer Schulze-Pillot
PublisherAmerican Mathematical Society
Pages391 - 397
Number of pages7
VolumeContemporary Mathematics 493
ISBN (Print)9780821846483
Publication statusPublished - 2009

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    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