J眉rgen Kl眉ners (Universit盲t Paderborn)
Title:听 Enumerating Orders in Number Fields
听
Abstract:听For a given number field K we study the distribution of suborders of the maximal order O_K of K. The Chinese Remainder Theorem shows that it suffices to describe the orders whose index in O_K is a power of p for some prime p.
Zassenhaus' well-known Round 2 algorithm yields an effective method to compute the p-maximal order of a given order in K. We show how to reverse this process to enumerate the orders of a given prime power index in O_K.
On the one hand, we get an algorithm which is implemented in the computer algebra system OSCAR. On the other hand, our approach highlights structures which allow us to describe the distribution of suborders whose index is a prime power in an explicit way. This is joint work with Markus Kirschmer.
Location:听University of Montreal AA-6214