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This document proves the Duffin–Schaeffer conjecture for systems of m linear forms in n variables, establishing a criterion for the approximation of these systems using integer vectors under a coprimality condition. The results generalize previous work on the classical conjecture and its higher-dimensional versions, with implications for Hausdorff measure analogues. The paper also discusses the context of metric Diophantine approximation and related theorems, highlighting the significance of the conjecture

Author

Hamada Routbi

Language

EN