NOTES ON THE K-RATIONAL DISTANCE PROBLEM

Let K be an algebraic number field. We investigate the K-rational distance problem and prove that there are infinitely many nonisomorphic cubic number fields and a number field of degree n for every $n\geq 2$ in which there is a point in the plane of a unit square at K-rational distances from the fo...

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Veröffentlicht in:	Bulletin of the Australian Mathematical Society 2021-08, Vol.104 (1), p.40-44
1. Verfasser:	THO, NGUYEN XUAN
Format:	Artikel
Sprache:	eng
Schlagworte:	Apexes Mathematics Number theory Physical Sciences Science & Technology
Online-Zugang:	Volltext
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Zusammenfassung:	Let K be an algebraic number field. We investigate the K-rational distance problem and prove that there are infinitely many nonisomorphic cubic number fields and a number field of degree n for every $n\geq 2$ in which there is a point in the plane of a unit square at K-rational distances from the four vertices of the square.
ISSN:	0004-9727 1755-1633
DOI:	10.1017/S0004972720001288