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Published online by Cambridge University Press: 24 October 2008
Suppose that K is a number field and n = [K: ℚ]. Write S∞(K) for the set of archimedean places of K, i.e. the set of all embeddings σ: K → ℂ. Suppose that is a linear form in t variables x1, …, xt, where the aj ∈ K. This gives rise to a norm form N(x), where