Lattice points in elliptic paraboloids

2016/11/14 by Fernando Chamizo, Chamizo, Fernando, Carlos Pastor +1
Mathematics · #Advanced Harmonic Analysis Research #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1611.04498

15 pages, added more precise Ω-results

openalex publication_date 2016/11/14 · arxiv created 2017/12/18 · arxiv updated 2017/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We consider the lattice point problem corresponding to a family of elliptic paraboloids in ℝ^d with d≥3 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 Ω-result that is unknown for the classical circle and divisor problems.

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