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Showing 1 to 1 of 1 for “"Three Gap Theorem"”.
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Beatty ratios, algorithms related to Sturmian sequences and uniform distribution theory
This dissertation is divided into three main sections. The main result of Section 1 is that, for $a,b>1$, irrational, the quantity $\log (a/b)$ is ``not too far'' from the series of fractional parts $$ \sum_{n=1}^{\infty}\frac{a \{a^{-1} (n+1)\}-b\{b^{-1}(n+1)\}}{n(n+1)} \text{,}$$ i.e, the …