Open Access
2019 Lattice points in elliptic paraboloids
Fernando Chamizo, Carlos Pastor
Publ. Mat. 63(1): 343-360 (2019). DOI: 10.5565/PUBLMAT6311912


We consider the lattice point problem corresponding to a family of elliptic paraboloids in $\mathbb{R}^d$ with $d\ge3$ and we prove the expected to be optimal exponent, improving previous results. This is especially noticeable for $d=3$ because the optimal exponent is conjectural even for the sphere. We also treat some aspects of the case $d=2$, getting for a simple parabolic region an $\Omega$-result that is unknown for the classical circle and divisor problems.


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Fernando Chamizo. Carlos Pastor. "Lattice points in elliptic paraboloids." Publ. Mat. 63 (1) 343 - 360, 2019.


Received: 4 September 2017; Revised: 30 January 2018; Published: 2019
First available in Project Euclid: 7 December 2018

zbMATH: 07040972
MathSciNet: MR3908797
Digital Object Identifier: 10.5565/PUBLMAT6311912

Primary: 11L07 , 11P21

Keywords: elliptic paraboloids , exponential sums , lattice point problem

Rights: Copyright © 2019 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.63 • No. 1 • 2019
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