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arXiv · 1805.01508

First Moment of Distances Between Centres of Ford Spheres

Kayleigh Measures
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Abstract

This paper aims to develop the theory of Ford spheres in line with the current theory for Ford circles laid out in a recent paper by S. Chaubey, A. Malik and A. Zaharescu. As a first step towards this goal, we establish an asymptotic estimate for the first moment $\mathcal{M}_{1,I_2} (S) = \sum\limits_{\substack{\frac{r}{s},\frac{r'}{s'}\in \mathcal{G}_S \\ consec}} \frac{1}{2\lvert s \rvert ^2} + \frac{1}{2\lvert s' \rvert ^2}$ where the sum is taken over pairs of fractions associated with `consecutive' Ford spheres of radius less than or equal to $\frac{1}{2S^2}$.

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Kayleigh Measures. 2018-05-03. First Moment of Distances Between Centres of Ford Spheres. https://arxiv.org/abs/1805.01508

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