Diophantine FLINT-HILLS series
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912221752197120 |
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| author | Mantzakouras, Nikos Zapata, Carlos López |
| author_facet | Mantzakouras, Nikos Zapata, Carlos López |
| contents | We prove the convergence of the FLINT-HILLS series and establish new criteria for a similar type of diophantine or lacunary series, which faces issues due to spaced long terms coming from the trigonometric nature of functions, e.g., cosecant in the FLINT-HILLS series. We connect the FLINT-HILLS series to the Fermi-Dirac integral via the Riemann-Stieltjes integral and YOUNG'S inequality criteria but also proved that the upper bound of the irrationality measure of pi is equal or lower than 2.5 expected if the FLINT-HILLS series converged. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03474 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Diophantine FLINT-HILLS series Mantzakouras, Nikos Zapata, Carlos López General Mathematics We prove the convergence of the FLINT-HILLS series and establish new criteria for a similar type of diophantine or lacunary series, which faces issues due to spaced long terms coming from the trigonometric nature of functions, e.g., cosecant in the FLINT-HILLS series. We connect the FLINT-HILLS series to the Fermi-Dirac integral via the Riemann-Stieltjes integral and YOUNG'S inequality criteria but also proved that the upper bound of the irrationality measure of pi is equal or lower than 2.5 expected if the FLINT-HILLS series converged. |
| title | Diophantine FLINT-HILLS series |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2502.03474 |