Lattice points in stretched finite type domains

2021/11/11 by Jin Yun Guo, Guo, J., Tianshu Jiang +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2111.06244

openalex publication_date 2021/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study an optimal stretching problem, which is a variant lattice point problem, for convex domains in ℝ^d (d≥ 2) with smooth boundary of finite type that are symmetric with respect to each coordinate hyperplane/axis. We prove that optimal domains which contain the most positive (or least nonnegative) lattice points are asymptotically balanced.

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