S. Corinne Hutchinson and Alexandru Zaharescu: Parabolas infiltrating the Ford circles, p.175-185

Abstract:

We define and study a new family of parabolas in connection with Ford circles and discover some interesting properties that they have. Using these properties, we provide an application of such a family. This application, which establishes an asymptotic estimate for the $L^2$ norm of a set of parabolas, proves useful in connection with recent work done by Kunik.

Key Words: Ford circles, Parabolas, Farey fractions.

2000 Mathematics Subject Classification: Primary: 11B57;
Secondary: 11B99.