Integer continued fractions for complex numbers
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911113637003264 |
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| author | O'Sullivan, Cormac |
| author_facet | O'Sullivan, Cormac |
| contents | We study a natural extension to complex numbers of the standard continued fractions. The basic algorithm is due to Lagrange and Gauss, though it seems to have gone mostly unnoticed as a way to create continued fractions. The new representations are shown to be unique, and to have useful properties. They also admit a geometric cutting sequence interpretation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15078 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integer continued fractions for complex numbers O'Sullivan, Cormac Number Theory 11Y65, 11F06, 11H55 We study a natural extension to complex numbers of the standard continued fractions. The basic algorithm is due to Lagrange and Gauss, though it seems to have gone mostly unnoticed as a way to create continued fractions. The new representations are shown to be unique, and to have useful properties. They also admit a geometric cutting sequence interpretation. |
| title | Integer continued fractions for complex numbers |
| topic | Number Theory 11Y65, 11F06, 11H55 |
| url | https://arxiv.org/abs/2508.15078 |