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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