Shapes of Multiquadratic Extensions

Date
2019
Authors
Hassan Haidar, Jamal Hassan
Contributor
Advisor
Harron, Robert
Department
Mathematics
Instructor
Depositor
Speaker
Researcher
Consultant
Interviewer
Annotator
Journal Title
Journal ISSN
Volume Title
Publisher
Volume
Number/Issue
Starting Page
Ending Page
Alternative Title
Abstract
For a positive integer $n$, we compute the shape of a totally real multiquadratic extension of degree $2^n$ in which the prime $2$ does not ramify. From this calculation, we see that the shape of such a number field is parametrized by the generators of its $2^n-1$ quadratic subfields. Restricting to the case $n=3$, we use this parametrization to count the number of triquadratic extensions of bounded discriminant and bounded shape parameters. We then show that, as the discriminant goes to infinity, these shapes become equidistributed in a regularized sense in the subset of the space of shapes of rank $7$ lattices that contains them.
Description
Keywords
Mathematics, Equidistribution, Multiquadratic, Shape
Citation
Extent
64 pages
Format
Geographic Location
Time Period
Related To
Table of Contents
Rights
Rights Holder
Local Contexts
Email libraryada-l@lists.hawaii.edu if you need this content in ADA-compliant format.