Random Aharonov-Bohm vortices and some exactly solvable families of integrals
Résumé
A review of the random magnetic impurity model, introduced in the context of the integer Quantum Hall effect, is presented. It models an electron moving in a plane and coupled to random Aharonov-Bohm vortices carrying a fraction of the quantum of flux. Recent results on its perturbative expansion are given. In particular, some funny families of integrals show up to be related to the Riemann $\\zeta(3)$ and $\\zeta(2)$.