Multiple Legendre polynomials in Diophantine approximation
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908711663960064 |
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| author | Marcovecchio, Raffaele |
| author_facet | Marcovecchio, Raffaele |
| contents | We construct a class of multiple Legendre polynomials and prove that they satisfy an Apéry-like recurrence. We give new upper bounds of the approximation measures of logarithms of rational numbers by algebraic numbers of bounded degree. We prove e.g. that the nonquadraticity exponent of $\log 2$ is bounded from above by $12.841618...$, thus improving upon a recent result of the author. Our construction also yields some other known results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12890 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiple Legendre polynomials in Diophantine approximation Marcovecchio, Raffaele Number Theory 11J82, 11J04, 11J17, 33C45 We construct a class of multiple Legendre polynomials and prove that they satisfy an Apéry-like recurrence. We give new upper bounds of the approximation measures of logarithms of rational numbers by algebraic numbers of bounded degree. We prove e.g. that the nonquadraticity exponent of $\log 2$ is bounded from above by $12.841618...$, thus improving upon a recent result of the author. Our construction also yields some other known results. |
| title | Multiple Legendre polynomials in Diophantine approximation |
| topic | Number Theory 11J82, 11J04, 11J17, 33C45 |
| url | https://arxiv.org/abs/2512.12890 |