On a reciprocity theorem of Gauss

LH Walling

On a reciprocity theorem of Gauss

LH Walling

Research output: Chapter in Book/Report/Conference proceeding › Chapter 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 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

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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

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title = "On a reciprocity theorem of Gauss",

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.",

author = "LH Walling",

year = "2009",

language = "English",

isbn = "9780821846483",

volume = "Contemporary Mathematics 493",

pages = "391 -- 397",

editor = "Ricardo Baeza and Chan, \{Wai Kiu\} and Hoffmann, \{Detlev W.\} and Rainer Schulze-Pillot",

booktitle = "Quadratic Forms--Algebra, Arithmetic, and Geometry",

publisher = "American Mathematical Society",

address = "United States",

}

Walling, LH 2009, On a reciprocity theorem of Gauss. in R Baeza, WK Chan, DW Hoffmann & R Schulze-Pillot (eds), Quadratic Forms--Algebra, Arithmetic, and Geometry. vol. Contemporary Mathematics 493, American Mathematical Society, pp. 391 - 397. <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>

TY - CHAP

T1 - On a reciprocity theorem of Gauss

AU - Walling, LH

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

M3 - Chapter in a book

SN - 9780821846483

VL - Contemporary Mathematics 493

SP - 391

EP - 397

BT - Quadratic Forms--Algebra, Arithmetic, and Geometry

A2 - Baeza, Ricardo

A2 - Chan, Wai Kiu

A2 - Hoffmann, Detlev W.

A2 - Schulze-Pillot, Rainer

PB - American Mathematical Society

ER -

On a reciprocity theorem of Gauss

Abstract

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