Email this article Some applications of growth in $\mathrm{SL}_2(\pmb{\mathbb{F}}_p)$ to the proof of modular versions of Zaremba's conjecture
- Authors: Lyamkin M.V.1
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Affiliations:
- Steklov Mathematical Institute of Russian Academy of Sciences
- Issue: Vol 213, No 10 (2022)
- Pages: 108-129
- Section: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/133472
- DOI: https://doi.org/10.4213/sm9707
- ID: 133472
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Abstract
Using growth in $\mathrm{SL}_2(\mathbb{F}_p)$ we prove that for every prime number $p$ and any positive integer $u$ there are positive integers $q=O(p^{2+\varepsilon})$, $\varepsilon > 0$, $q \equiv u \pmod{p}$, and $a < p$, $(a, p)=1$, such that the partial quotients of the continued fraction of $a/q$ are bounded by an absolute constant.Bibliography: 21 titles.
About the authors
Mikhail Vladimirovich Lyamkin
Steklov Mathematical Institute of Russian Academy of Scienceswithout scientific degree, no status
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