On two lattice points problems about the parabola release_szyufo7kmnbb5ncj2g4xfmovty

by Jing-Jing Huang, Huixi Li

Released as a article .

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.
In text/plain format

Archived Files and Locations

application/pdf  151.1 kB
file_pwo5anvs2nfetoha5uk5cm5vpu
arxiv.org (repository)
web.archive.org (webarchive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   submitted
Date   2019-02-16
Version   v1
Language   en ?
arXiv  1902.06047v1
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: 95e6e30f-cd7c-4a31-815f-90fefe20035a
API URL: JSON