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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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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 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.

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

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References

1.Halberstam, H. and Richert, H.-E.. Sieve methods (Academic Press, London-New York-San Francisco, 1974).Google Scholar
2.Hinz, J. G.. On the theorem of Barban and Davenport-Halberstam in algebraic number fields. J. of Number Theory, 13 (1981), 463–484.Google Scholar
3.Hinz, J. G.. Eine Anwendung der Selbergschen Siebmethode in algebraischen Zahlkörpern. Ada Arith., 41.Google Scholar
4.Rademacher, H.. Über die Anwendung der Viggo Brunschen Methode auf die Theorie der algebraischen Zahlkörper. Sitzungsber. Preuss. Akad. Wiss., Phys.-Math. Klasse, (1923), 211–218.Google Scholar
5.Schaal, W.. Obere und untere Abschätzungen in algebraischen Zahlkörpern mit Hilfe des linearen Selbergschen Siebes. Acta Arith., 13 (1968), 267–313.CrossRefGoogle Scholar
6.Siegel, C. L.. Additive Theorie der Zahlkörper II. Math. Ann., 88 (1923), 184–210.CrossRefGoogle Scholar
7.Vinogradov, A. I.. The sieve method in algebraic fields. Lower bounds (Russian). Mat. Sbornik (N.S.), 64 (106), (1964), 52–78.Google Scholar