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First moment of distances between centres of Ford spheres.
- Source :
-
Journal of Mathematical Analysis & Applications . Oct2019, Vol. 478 Issue 2, p1100-1120. 21p. - Publication Year :
- 2019
-
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 M 1 , I 2 (S) = ∑ r s , r ′ s ′ ∈ G S c o n s e c 1 2 | s | 2 + 1 2 | s ′ | 2 , where the sum is taken over pairs of fractions associated with 'consecutive' Ford spheres of radius less than or equal to 1 2 S 2 . [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 478
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 137250591
- Full Text :
- https://doi.org/10.1016/j.jmaa.2019.06.004