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Some applications of growth in $\mathrm{SL}_2(\pmb{\mathbb{F}}_p)$ to the proof of modular versions of Zaremba's conjecture
Sbornik. Mathematics, Tome 213 (2022) no. 10, pp. 1415-1435 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: continued fractions, growth in groups.
Mots-clés : Zaremba conjecture 
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M. V. Lyamkin. Some applications of growth in $\mathrm{SL}_2(\pmb{\mathbb{F}}_p)$ to the proof of modular versions of Zaremba's conjecture. Sbornik. Mathematics, Tome 213 (2022) no. 10, pp. 1415-1435. http://geodesic.mathdoc.fr/item/SM_2022_213_10_a3/

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