Fast norm computation in smooth-degree Abelian number fields

• Published in: Research in number theory Vol. 9; no. 4
• Main Author: Bernstein, Daniel J.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.12.2023; Springer Nature B.V
• Subjects: Algorithms; Computation; Fifteenth Algorithmic Number Theory Symposium (ANTSXV); Fractions; Mathematics; Mathematics and Statistics; Multiplication; Norms; Number Theory; Searching; Towers; 11R18; 11Y16; Primary 11Y40; Secondary 68W30

This paper presents a fast method to compute algebraic norms of integral elements of smooth-degree cyclotomic fields, and, more generally, smooth-degree Galois number fields with commutative Galois groups. The typical scenario arising in S -unit searches (for, e.g., class-group computation) is compu...