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Shapes of Multiquadratic Extensions

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Item Summary

Title:Shapes of Multiquadratic Extensions
Authors:Hassan Haidar, Jamal Hassan
Contributors:Harron, Robert (advisor)
Mathematics (department)
Keywords:Mathematics
Equidistribution
Multiquadratic
Shape
Date Issued:2019
Publisher:University of Hawai'i at Manoa
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.
Pages/Duration:64 pages
URI:http://hdl.handle.net/10125/63501
Appears in Collections: Ph.D. - Mathematics


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