Approximating Good Simultaneous Diophantine Approximations Is Almost NP-Hard

Given a real vector α=(α1,..., α d ) and a real number e>0 a good Diophantine approximation to α is a number Q such that ∥Qα mod ℤ∥∞ ≤e, where ∥ · ∥∞ denotes the l∞-norm ∥x∥t8 ≔ max1 ≤i≤d ¦ xi¦ for x=(x1,..., xd).

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