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@article{Crowdy:2021,
author = {Crowdy, D and MIYOSHI, H and Nelson, R},
journal = {Computational Methods and Function Theory - Springer},
pages = {707--736},
title = {The prime function, the Fay trisecant identity, andthe van der Pauw method. On some conjectures on the resistivity of a holey conductor},
url = {https://link.springer.com/article/10.1007%2Fs40315-021-00409-1},
volume = {21},
year = {2021}
}

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TY  - JOUR
AB  - The van der Pauw method is a well-known experimental techniquein the applied sciences for measuring physical quantities such as the electricalconductivity or the Hall coefficient of a given sample. Its popularity isattributable to its flexibility: the same method works for planar samples ofany shape provided they are simply connected. Mathematically, the method isbased on the cross-ratio identity. Much recent work has been done by appliedscientists attempting to extend the van der Pauw method to samples withholes (“holey samples”). In this article we show the relevance of two newfunction theoretic ingredients to this area of application: the prime functionassociated with the Schottky double of a multiply connected planar domainand the Fay trisecant identity involving that prime function. We focus hereon the single-hole (doubly connected, or genus one) case. Using these newtheoretical ingredients we are able to prove several mathematical conjecturesput forward in the applied science literature.
AU  - Crowdy,D
AU  - MIYOSHI,H
AU  - Nelson,R
EP  - 736
PY  - 2021///
SN  - 1617-9447
SP  - 707
TI  - The prime function, the Fay trisecant identity, andthe van der Pauw method. On some conjectures on the resistivity of a holey conductor
T2  - Computational Methods and Function Theory - Springer
UR  - https://link.springer.com/article/10.1007%2Fs40315-021-00409-1
UR  - http://hdl.handle.net/10044/1/90758
VL  - 21
ER  -

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