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Lethbridge Number Theory and Combinatorics Seminar
February 12, 2018
Ha Tran (University of Calgary)
University of Lethbridge
Reduced Ideals from the Reduction Algorithm
Description (in plain text format):
Reduced ideals of a number field F have inverses of small norms and they form a finite and regularly distributed set in the infrastructure of F. Therefore, they can be used to compute the regulator and the class number of a number field. One usually applies the reduction algorithm to find them. Ideals obtained from this algorithm are called 1-reduced. There exist reduced ideals that are not 1-reduced.
We will show that these ideals have inverses of larger norms among reduced ones. Especially, we represent a sufficient and necessary condition for reduced ideals of real quadratic fields to be obtained from the reduction algorithm.
Location: B543 University Hall