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 momentM1,I2(S)=∑rs,r′s′∈GSconsec12|s|2+12|s′|2, where the sum is taken over pairs of fractions associated with ‘consecutive’ Ford spheres of radius less than or equal to 12S2.

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