A Magnetic Double Integral

Broadhurst, David and Zudilin, Wadim (2019). A Magnetic Double Integral. Journal of the Australian Mathematical Society, 107(1) pp. 9–25.

DOI: https://doi.org/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, U. Ausserlechner has come up with a remarkable double integral that can be viewed as a generalisation of the classical elliptic ‘arithmetic–geometric mean (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.

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