On two lattice points problems about the parabola [article]

Jing-Jing Huang, Huixi Li
2019 arXiv   pre-print
We obtain asymptotic formulae with optimal error terms for the number of lattice points under and near a dilation of the standard parabola, the former improving upon an old result of Popov. These results can be regarded as achieving the square root cancellation in the context of the parabola, whereas its analogues are wide open conjectures for the circle and the hyperbola. We also obtain essentially sharp upper bounds for the latter lattice points problem. Our proofs utilize techniques in
more » ... r analysis, quadratic Gauss sums and character sums.
arXiv:1902.06047v1 fatcat:szyufo7kmnbb5ncj2g4xfmovty