#### Vol. 2, 2019

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Explicit computations in Iwasawa theory

### Reinier Bröker, David Hubbard and Lawrence C. Washington

Vol. 2 (2019), No. 1, 137–153
##### Abstract

We give two algorithms to compute layers of the anticyclotomic ${ℤ}_{3}$-extension of an imaginary quadratic field. The first is based on complex multiplication techniques for nonmaximal orders; the second is based on Kummer theory. As an illustration of our results, we use the mirroring principle to derive results on the structure of class groups of nonmaximal orders.

##### Keywords
anticyclotomic, Iwasawa theory, nonmaximal order
Primary: 11R23
Secondary: 14K22
##### Supplementary material

Magma code to compute the examples discussed

##### Milestones
Received: 19 February 2018
Revised: 9 September 2018
Accepted: 10 September 2018
Published: 13 February 2019
##### Authors
 Reinier Bröker Center for Communications Research Princeton, NJ United States David Hubbard Hamilton, NJ United States Lawrence C. Washington Department of Mathematics University of Maryland College Park, MD United States