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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.12299 |
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| _version_ | 1866918141523656704 |
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| author | Castillo, A. E. D. Lobos, G. A. Batista, V. Ramos |
| author_facet | Castillo, A. E. D. Lobos, G. A. Batista, V. Ramos |
| contents | 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 Weierstraß\,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-Weierstraß\,function, and these resources simplify the computation of elliptic functions considerably. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12299 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Green's Function on Rhombic Flat Tori Castillo, A. E. D. Lobos, G. A. Batista, V. Ramos Numerical Analysis 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 Weierstraß\,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-Weierstraß\,function, and these resources simplify the computation of elliptic functions considerably. |
| title | The Green's Function on Rhombic Flat Tori |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2509.12299 |