@article {31883,
	title = {Diophantine approximation with constraints},
	journal = {Acta Arithmetica},
	volume = {207},
	year = {2023},
	pages = {57-99},
	abstract = {Following Schmidt, Thurnheer and Bugeaud{\textendash}Kristensen, we study how Dirichlet{\textquoteright}s theorem on linear forms needs to be modified when one requires that the vectors of coefficients of the linear forms make a bounded acute angle with respect to a fixed proper non-zero subspace\&nbsp;V\&nbsp;of\&nbsp;ℝ<sup>n</sup>. Assuming that the point of\&nbsp;ℝ<sup>n</sup> that we are approximating has linearly independent coordinates over\&nbsp;ℚ, we obtain best possible exponents of approximation which surprisingly depend only on the dimension of\&nbsp;V. Our estimates are derived by reduction to a result of Thurnheer, while their optimality follows from a new general construction in parametric geometry of numbers involving angular constraints.},
	url = {https://www.impan.pl/en/publishing-house/journals-and-series/acta-arithmetica/all/207/1/115024/diophantine-approximation-with-constraints},
	author = {J{\'e}r{\'e}my Champagne and Damien Roy}
}
