Higher moments of distances between consecutive Ford spheres

JOURNAL OF NUMBER THEORY

卷:212

Article

Haynes, Alan¹  Measures, Kayleigh² 

[1] Univ Houston, Dept Math, Houston, TX 77204 USA

[2] Univ York, Dept Math, York YO10 5DD, N Yorkshire, England

关键词: Farey fractions;    Ford spheres;    Gauss circle problem;   

DOI  :  10.1016/j.jnt.2019.10.022

来源: Elsevier

【 摘 要 】

In previous work the second author derived an asymptotic formula for the sum of the distances between centers of consecutive Ford spheres. In this paper we extend these results by proving asymptotic formulas for higher moments of the distances. Our proofs rely on lattice point counting estimates with error terms coming from the Gauss circle problem. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free