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Guo, Jingwei

Lattice points in large convex planar domains of finite type. (English) Zbl 1327.11065

Ill. J. Math. 56, No. 3, 731-757 (2012).
Summary: Let \(\mathcal{B}\) be a compact convex planar domain with 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.

Cited in 4 Documents

MSC:

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

Keywords:

lattice point; convex planar domain of finite type; Fourier transform; exponential sum
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References:

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