Séminaire Lotharingien de Combinatoire, B22g (1989), 20 pp.
[Formerly: Publ. I.R.M.A. Strasbourg, 1990, 414/S-22, p.
51-70.]
Dominique Dumont
Résidus quadratiques et nombres de classes
Abstract.
Let p be a prime number congruent to 3 modulo 4. A classical formula
of Dirichlet relates the surplus of the residues over the non-residues in the
interval [1,(p-1)/2] to the class number h(-p). It is
still an open problem how to give a direct and non-analytic proof of this result.
We give here a detailed and elementary presentation of the subject, as well as
an analytic proof where the theory of divergent series enters naturally.
The following version is available: