The Number of Integers n in an Interval such that a ℓ n+b ℓ , ≤ ℓ ≤ m , are Norms of Ideals of a Number Field

Let [Formula: see text] be a number field, [Formula: see text] a real number, and [Formula: see text] integers. Let [Formula: see text] and [Formula: see text] be sequences of integers such that [Formula: see text] and [Formula: see text] for all 1 [Formula: see text]. We give an upper bound for the number of integers [Formula: see text] for which [Formula: see text], for each [Formula: see text], is the norm of an ideal of the ring of integers of [Formula: see text]. This result extends to arbi