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A review of the random magnetic impurity model, introduced in the context ofthe integer Quantum Hall effect, is presented. It models an electron moving ina plane and coupled to random Aharonov-Bohm vortices carrying a fraction of thequantum of flux. Recent results on its perturbative expansion are given. Inparticular, some funny families of integrals show up to be related to theRiemann $\zeta(3)$ and $\zeta(2)$.Comment: 10 page

Random Aharonov–Bohm vortices and some exactly solvable families of integrals