Indecomposable totally positive numbers in real quadratic orders

Dress A, Scharlau R (1982)
Journal of Number Theory 14(3): 292-306.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Dress, AndreasUniBi; Scharlau, Rudolf
Abstract / Bemerkung
In a totally real number field, every totally positive integral number is a finite sum of (additively) indecomposable totally positive integral numbers, and up to multiplication by totally positive units, there exist only finitely many indecomposables. In the paper it is shown that in quadratic fields all these numbers can be listed in a very efficient way by using the so-called intermediate convergents of a certain quadratic irrationality. The method can be viewed as a simple extension of the standard method of calculating the fundamental unit by using continued fractions. As an application it is shown that for instance in Z|√d| a number is decomposable if its norm is >d. It is remarkable that this bound does not depend on the size of the fundamental unit.
Erscheinungsjahr
1982
Zeitschriftentitel
Journal of Number Theory
Band
14
Ausgabe
3
Seite(n)
292-306
ISSN
0022-314X
Page URI
https://pub.uni-bielefeld.de/record/1660741

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Dress A, Scharlau R. Indecomposable totally positive numbers in real quadratic orders. Journal of Number Theory. 1982;14(3):292-306.
Dress, A., & Scharlau, R. (1982). Indecomposable totally positive numbers in real quadratic orders. Journal of Number Theory, 14(3), 292-306. https://doi.org/10.1016/0022-314X(82)90064-6
Dress, A., and Scharlau, R. (1982). Indecomposable totally positive numbers in real quadratic orders. Journal of Number Theory 14, 292-306.
Dress, A., & Scharlau, R., 1982. Indecomposable totally positive numbers in real quadratic orders. Journal of Number Theory, 14(3), p 292-306.
A. Dress and R. Scharlau, “Indecomposable totally positive numbers in real quadratic orders”, Journal of Number Theory, vol. 14, 1982, pp. 292-306.
Dress, A., Scharlau, R.: Indecomposable totally positive numbers in real quadratic orders. Journal of Number Theory. 14, 292-306 (1982).
Dress, Andreas, and Scharlau, Rudolf. “Indecomposable totally positive numbers in real quadratic orders”. Journal of Number Theory 14.3 (1982): 292-306.

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