Application of the large sieve to the solution of additive problems of mixed type

A variant of the large-sieve: method, using a combination of results obtained by Lavrik, Montgomery, and Eombieri, is employed to derive asymptotic properties of the number of solutions of the equationNp+Na=n wherep is a prime ideal of some ideal class of a field K of degree n4, anda is a prime ideal of a class of an imaginary quadratic field.Translated from Matematicheskie Zametki, Vol. 10, No. 1, pp. 73–81, July, 1971.The author wishes to thank A. I. Vinogradov for his help and advice in this work.