Illinois Journal of Mathematics

Lattice points in large convex planar domains of finite type

Jingwei Guo

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Abstract

Let $\mathcal{B}$ be a compact convex planar domain with[4] smooth boundary of finite type and $\mathcal{B}_{\theta}$ its rotation by an angle $\theta$. We prove that for almost every $\theta\in[0,2\pi]$ the remainder $P_{\mathcal{B}_{\theta}}(t)$ is of order $O_{\theta}(t^{2/3-\zeta})$ with a positive number $\zeta$ independent of the domain.

Article information

Source
Illinois J. Math., Volume 56, Number 3 (2012), 731-757.

Dates
First available in Project Euclid: 31 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1391178546

Digital Object Identifier
doi:10.1215/ijm/1391178546

Mathematical Reviews number (MathSciNet)
MR3161349

Zentralblatt MATH identifier
1327.11065

Subjects
Primary: 11P21: Lattice points in specified regions 11L07: Estimates on exponential sums
Secondary: 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type

Citation

Guo, Jingwei. Lattice points in large convex planar domains of finite type. Illinois J. Math. 56 (2012), no. 3, 731--757. doi:10.1215/ijm/1391178546. https://projecteuclid.org/euclid.ijm/1391178546


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