A Geometric-Arithmetic Framework for the Flint Hills Series
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917052543926272 |
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| author | Garab, Mohammed-Adnane |
| author_facet | Garab, Mohammed-Adnane |
| contents | We introduce a geometric-arithmetic approach to the analysis of the Flint Hills series, linking its convergence behavior to the irrationality measure of pi. The framework highlights the interplay between the distribution of near-multiples of pi and the growth rate of denominator sequences, offering new insights into the arithmetic structure underlying this famous unsolved problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_27041 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Geometric-Arithmetic Framework for the Flint Hills Series Garab, Mohammed-Adnane Number Theory 11J82, 11K60 11J82, 11K60 11J82, 11K60 11J82, 11K60 We introduce a geometric-arithmetic approach to the analysis of the Flint Hills series, linking its convergence behavior to the irrationality measure of pi. The framework highlights the interplay between the distribution of near-multiples of pi and the growth rate of denominator sequences, offering new insights into the arithmetic structure underlying this famous unsolved problem. |
| title | A Geometric-Arithmetic Framework for the Flint Hills Series |
| topic | Number Theory 11J82, 11K60 11J82, 11K60 11J82, 11K60 11J82, 11K60 |
| url | https://arxiv.org/abs/2510.27041 |