The large sieve in algebraic number fields

The objectjof this paper is to extend to algebraic number fields some of the recent results proved by the large sieve method. In particular we prove generalizations of Bombieri's form of the large sieve inequality [1; Theorem 1] and of the theorems of Davenport and Halberstam [2] and Bombieri [1, 4], on the average distribution of primes in arithmetic progressions.