English

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

Number Theory 2023-07-19 v1 Analysis of PDEs

Abstract

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

Keywords

Cite

@article{arxiv.1503.06719,
  title  = {$L^{p}$ and Weak-$L^{p}$ estimates for the number of integer points in translated domains},
  author = {Luca Brandolini and Leonardo Colzani and Giacomo Gigante and Giancarlo Travaglini},
  journal= {arXiv preprint arXiv:1503.06719},
  year   = {2023}
}