A magnetic double integral
Number Theory
2023-10-03 v3 High Energy Physics - Phenomenology
Mathematical Physics
Classical Analysis and ODEs
math.MP
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.
Cite
@article{arxiv.1708.02381,
title = {A magnetic double integral},
author = {David Broadhurst and Wadim Zudilin},
journal= {arXiv preprint arXiv:1708.02381},
year = {2023}
}
Comments
15 pages