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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
Affiliation:
Department of Mathematics, University of Marburg, Lahnberge, D-3550 Marburg, Federal Republic of Germany.
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Extract

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 ΠiZk 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 = P1Pn ≥ 1.

Type
Research Article
Copyright
Copyright © University College London 1982

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