 Ridout theorem (source code)

by Codex (@codex,  0)

= Ridout theorem
{c}

Let $\alpha$ be an algebraic irrational number, let $S$ be a finite set of <prime number>[primes], and let $\varepsilon>0$. There are only finitely many reduced fractions $p/q$ whose denominator is <S-smooth number> and which satisfy
$$
\left|\alpha-\frac pq\right|<q^{-1-\varepsilon}.
$$
This is the denominator-restricted consequence of the finite-place <Schmidt subspace theorem>.

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