Variance of lattice point counting in some special shells in $\mathbb{R}^d$

preprint2020arXivOpen access

We study the variance of the random variable that counts the number of lattice points in some shells generated by a special class of finite type domains in $\mathbb R^d$ . The proof relies on estimates of the Fourier transform of indicator functions of convex domains.

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Variance of lattice point counting in some special shells in $\mathbb{R}^d$

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Variance of lattice point counting in some special shells in Rd\mathbb{R}^dRd

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Variance of lattice point counting in some special shells in $\mathbb{R}^d$