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$L^{p}$ and Weak-$L^{p}$ estimates for the number of integer points in translated domains

By Luca Brandolini, Leonardo Colzani, Giacomo Gigante and Giancarlo Travaglini

Abstract

Revisiting and extending a recent result of M.Huxley, we estimate the $L^{p}\left( \mathbb{T}^{d}\right) $ and Weak-$L^{p}\left( \mathbb{T}^{d}\right) $ norms of the discrepancy between the volume and the number of integer points in translated domains

Topics: Mathematics - Number Theory, Mathematics - Analysis of PDEs, 11H06, 52C07
Year: 2015
OAI identifier: oai:arXiv.org:1503.06719

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