The Shaping of Arithmetic after C. F. Gauss’s Disquisitiones Arithmeticae

Edited by Catherine Goldstein (), Norbert Schappacher () and Joachim Schwermer ()

in Springer Books from Springer

Date: 2007
ISBN: 978-3-540-34720-0
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Chapters in this book:

Ch I.1 A Book in Search of a Discipline (1801–1860)

Catherine Goldstein and Norbert Schappacher

Ch I.2 Several Disciplines and a Book (1860–1901)

Catherine Goldstein and Norbert Schappacher

Ch II.1 The Disquisitiones Arithmeticae and the Theory of Equations

Olaf Neumann

Ch II.2 Composition of Binary Quadratic Forms and the Foundations of Mathematics

Harold M. Edwards

Ch II.3 Composition of Quadratic Forms: An Algebraic Perspective

Della D. Fenster and Joachim Schwermer

Ch II.4 The Unpublished Section Eight: On the Way to Function Fields over a Finite Field

Günther Frei

Ch III.1 A Network of Scientific Philanthropy: Humboldt’s Relations with Number Theorists

Herbert Pieper

Ch III.2 ‘O Θɛòζ’ Aριθμηίíξɛι: The Rise of Pure Mathematics as Arithmetic with Gauss

José Ferreirós

Ch IV.1 From Reciprocity Laws to Ideal Numbers: An (Un)Known Manuscript by E.E. Kummer

Reinhard Bölling

Ch IV.2 Elliptic Functions and Arithmetic

Christian Houzel

Ch V.1 The Concept of Number from Gauss to Kronecker

Jacqueline Boniface

Ch V.2 On Arithmetization

Birgit Petri and Norbert Schappacher

Ch VI.1 The Hermitian Form of Reading the Disquisitiones

Catherine Goldstein

Ch VI.2 Number Theory at the Association française pour l’avancement des sciences

Anne-Marie Décaillot

Ch VII.1 An Overview on Italian Arithmetic after the Disquisitiones Arithmeticae

Aldo Brigaglia

Ch VII.2 Zolotarev’s Theory of Algebraic Numbers

Paola Piazza

Ch VII.3 Gauss Goes West: The Reception of the Disquisitiones Arithmeticae in the USA

Della Fenster

Ch VIII.1 Reduction Theory of Quadratic Forms: Towards Räumliche Anschauung in Minkowski’s Early Work

Joachim Schwermer

Ch VIII.2 Gauss Sums

Samuel James Patterson

Ch VIII.3 The Development of the Principal Genus Theorem

Franz Lemmermeyer

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DOI: 10.1007/978-3-540-34720-0

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