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On two lattice points problems about the parabola
release_szyufo7kmnbb5ncj2g4xfmovty
by
Jing-Jing Huang, Huixi Li
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2019
Abstract
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 Fourier analysis, quadratic Gauss
sums and character sums.
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1902.06047v1
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