Diophantine approximation on the parabola with non-monotonic approximation functions
Number Theory
2018-12-18 v2
Abstract
We show that the parabola is of strong Khintchine type for convergence, which is the first result of its kind for curves. Moreover, Jarnik type theorems are established in both the simultaneous and the dual settings, without monotonicity on the approximation function. To achieve the above, we prove a new counting result for the number of rational points with fixed denominators lying close to the parabola, which uses Burgess's bound on short character sums.
Cite
@article{arxiv.1802.00525,
title = {Diophantine approximation on the parabola with non-monotonic approximation functions},
author = {Jing-Jing Huang},
journal= {arXiv preprint arXiv:1802.00525},
year = {2018}
}
Comments
minor revision, to appear in Math. Proc. Cambridge Philos. Soc