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On the representation of even integers as sums of two almost-primes in algebraic number fields

Published online by Cambridge University Press:  26 February 2010

Jürgen G. Hinz
Jürgen G. Hinz
Affiliation:
Department of Mathematics, University of Marburg, Lahnberge, D-3550 Marburg, Federal Republic of Germany.
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Let K be an algebraic number field of degree n = rl + 2r2 (in the usual notation) over the rationals with discriminant d. Let ZK denote the ring of integers in K. It is usual to speak of an integer Πi ∈ Zk as an almost-prime of order l, if the principal ideal (Πi) has at most l prime ideal factors, counted according to multiplicity. Let P1, …, Pn be positive real numbers with Pk = Pk+r2, k = r1 + l, …, r1 + r2 and P = P1 … Pn ≥ 1.

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Type
Research Article
Information
Mathematika , Volume 29 , Issue 1 , June 1982 , pp. 93 - 108
Copyright
Copyright © University College London 1982

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