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

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 4pu = 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.