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arXiv · 2503.00973

Irregularities of distribution and Fourier transforms of multi-dimensional convex bodies

Luca Brandolini·Leonardo Colzani·Giancarlo Travaglini
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Abstract

W. Schmidt, H. Montgomery, and J. Beck proved a result on irregularities of distribution with respect to $d$-dimensional balls. In this paper, we extend their result to any $d$-dimensional convex body with a smooth boundary and finite order of contact. As an intermediate step, we prove a geometric inequality for the Fourier transform of the characteristic function of a convex body.

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Luca Brandolini, Leonardo Colzani, Giancarlo Travaglini. 2025-03-02. Irregularities of distribution and Fourier transforms of multi-dimensional convex bodies. https://arxiv.org/abs/2503.00973

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