Introduction. Let F be a number field and S ∞ the set of its infinite primes. Assume that #(S ∞ ) = r 1 + r 2 , where r 1 is the number of real places of F and r 2 is the number of complex places. An Arakelov divisor is a pair D = (J D , v), where J D is a fractional ideal of the ring of integers O F and v ∈ R S ∞ . We say that J D is the finite part of D, while v is the infinite part. We denote by N (J D ) the ordinary norm of J D as a fractional ideal, and we define the norm of D in the following way:
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