Discriminants of Number Fields

The discriminant of a number field is an important invariant measuring its size and ramification behavior. We will first recall classical results by Minkowski, Odlyzko, Serre, and Golod and Šafarevič about discriminants. We then discuss the relevance of number fields with small root discriminants to...

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Veröffentlicht in:	Jahresbericht der Deutschen Mathematiker-Vereinigung 2024, Vol.126 (3), p.167-177
1. Verfasser:	Bleher, Frauke M.
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematics Mathematics and Statistics Number theory Survey Article
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	The discriminant of a number field is an important invariant measuring its size and ramification behavior. We will first recall classical results by Minkowski, Odlyzko, Serre, and Golod and Šafarevič about discriminants. We then discuss the relevance of number fields with small root discriminants to cryptography.
ISSN:	0012-0456 1869-7135
DOI:	10.1365/s13291-024-00286-2