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arXiv · 2509.12299

The Green's Function on Rhombic Flat Tori

A. E. D. Castillo·G. A. Lobos·V. Ramos Batista
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Abstract

We obtain the Green's function $G$ for any flat rhombic torus $T$, always with numerical values of significant digits up to the fourth decimal place (noting that $G$ is unique for $|T|=1$ and $\int_TGdA=0$). This precision is guaranteed by the strategies we adopt, which include theorems such as the Legendre Relation, properties of the Weierstra\ss\,P-Function, and also the algorithmic control of numerical errors. Our code uses complex integration routines developed by H. Karcher, who also introduced the symmetric P-Weierstra\ss\,function, and these resources simplify the computation of elliptic functions considerably.

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A. E. D. Castillo, G. A. Lobos, V. Ramos Batista. 2025-09-15. The Green's Function on Rhombic Flat Tori. https://arxiv.org/abs/2509.12299

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