Dirichlet's calculation of Gauss sums (Q436513)

This is a very nicely written article on Dirichlet's evaluation of quadratic Gauss sums. The determination of the sign of quadratic Gauss sums is the cornerstone of what perhaps is Gauss's deepest proof of the quadratic reciprocity law. By using complex integrals and by interpreting some limits showing up in Dirichlet's proof in terms of distributions, the author manages to give a clean account of Dirichlet's ideas and points out various connections to finite Fourier transforms, Fourier series, Fresnel integrals and distributions.