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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/2510.20832 |
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| _version_ | 1866914111072239616 |
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| author | Lamby, Thomas Nicolay, Samuel |
| author_facet | Lamby, Thomas Nicolay, Samuel |
| contents | This article examines the Thomae function, a paradigmatic example of a function that is continuous on the irrationals and discontinuous elsewhere. Defined for a parameter $θ>0$, it exhibits a rich self-similar structure and intriguing regularity properties. After revisiting its fundamental characteristics, we analyze its Hölder continuity, emphasizing the interplay between its discrete spikes and its behavior on dense subsets of the real line. This study provides a refined perspective on the irregularity of the Thomae function, using classical analytical tools to elucidate its fractal nature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20832 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Thomae Function: Fractal Insights Lamby, Thomas Nicolay, Samuel General Mathematics 26A15, 26A16, 26A30 This article examines the Thomae function, a paradigmatic example of a function that is continuous on the irrationals and discontinuous elsewhere. Defined for a parameter $θ>0$, it exhibits a rich self-similar structure and intriguing regularity properties. After revisiting its fundamental characteristics, we analyze its Hölder continuity, emphasizing the interplay between its discrete spikes and its behavior on dense subsets of the real line. This study provides a refined perspective on the irregularity of the Thomae function, using classical analytical tools to elucidate its fractal nature. |
| title | The Thomae Function: Fractal Insights |
| topic | General Mathematics 26A15, 26A16, 26A30 |
| url | https://arxiv.org/abs/2510.20832 |