Article ID: CBB001253129

Cyclotomie et formes quadratiques dans l'œuvre arithmétique d'Augustin-Louis Cauchy (1829--1840) (2013)

unapi

Augustin-Louis Cauchy published most of his arithmetical research between 1829 and 1840. These are however only mentioned in some number theory history centered on reciprocity laws or on theory of algebraic numbers. They are described as containing some results similar to those of Gauss, Jacobi and Dirichlet but in a incomplete and disorganized way. The objective of this paper is to present an analysis of Cauchy's arithmetical texts published between 1829 and 1840 to show that they contain a rather consistent set of results related to quadratic forms 4pmu=x2+ny2 , where p is a prime and n a divisor of p-1 . We will also discuss the particular form of this body of texts and the strategy we used to find the guidelines of the work of Cauchy.

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Authors & Contributors
Ehrhardt, Caroline
Boucard, Jenny
Goldstein, Catherine
Spalt, Detlef D.
Radu, Mircea
Meo, M.
Journals
Archive for History of Exact Sciences
Revue d'Histoire des Mathématiques
Historia Mathematica
Bollettino di Storia delle Scienze Matematiche
Science in Context
Revue de Synthèse
Publishers
Sociedad Andaluza de Educación Matemática THALES
American Mathematical Society
Springer
Concepts
Mathematics
Algebra
Number theory; number concept
Arithmetic
Group theory
Science and society
People
Cauchy, Augustin Louis
Galois, Évariste
Lagrange, Joseph Louis
Gauss, Carl Friedrich
Hölder, Ludwig Otto
Grassmann, Robert
Time Periods
19th century
20th century
18th century
20th century, early
17th century
Places
France
Italy
Paris (France)
Great Britain
Turin (Italy)
Institutions
École Polytechnique, Paris
University of Chicago
Académie des Sciences, Paris
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