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 $\frac{ 1}{ 2S^2}$.
Categories: math.NT