  Weil has generalized the Riemann-von Mangoldt explicit formula linking the
prime numbers with the zeros of the zeta function to the set-up of a general
algebraic number field K and Dirichlet-Hecke L-function, revealing in the
process the role played by the completions (finite and infinite) of K. We show
how the local terms of these explicit formulae are explained by the dilaton
invariant ``conductor operator'' log(|x|) + log(|y|). We also check Weil's
positivity criterion under a support condition.
