Author

Savita S. Adhin

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Preprint Jul 2026

Sharpening Borel's result in Diophantine approximation

In this paper, we refine Borel's 1903 result in Diophantine approximation by providing sharper bounds for the minimum of three consecutive approximation coefficients $\Theta_n(x)$, defined for any real number $x$ with regular continued fraction (RCF) expansion $x=[0;a_1,a_2,\dots]$ as $\Theta_n = q_n^2\left| x-\frac{p_...

Savita S. Adhin, Ayreena Bakhtawar, C. Kraaikamp · 0 citations