  In a recent study of how the output voltage of a Hall plate is affected by
the shape of the plate and the size of its contacts, Udo Ausserlechner has come
up with a remarkable double integral that can be viewed as a generalization of
the classical elliptic "AGM" integral. Here we discuss transformation
properties of the integral, which were experimentally observed by
Ausserlechner, as well as its analytical and arithmetic features including
connections with modular forms.
