A magnetic double integral
arXiv:1708.02381 · doi:10.1017/S1446788718000186
Abstract
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.
15 pages