Skip to main content

On K-derived quartics and invariants of local fields


Abstract This dissertation will cover two topics. For the first, let $K$ be a number field. A $K$-derived polynomial $f(x) \in K[x]$ is a polynomial that

factors into linear factors over $K$, as do all of its derivatives. Such a polynomial

is said to be {\it proper} if

its roots are distinct. An unresolved question in the literature is

whether or not there exists a proper $\Q$-derived polynomial of degree 4. Some examples

are known of proper $K$-derived quartics for a quadratic number field $K$, although other

than $\Q(\sqrt{3})$, these fields have quite large discriminant. (The second known field

is $\Q(\sqrt{3441})$.) I will describe a search for quadratic fields $K$

over which there exist proper $K$-derived quartics. The search find... (more)
Created Date 2019
Contributor Carrillo, Benjamin (Author) / Jones, John (Advisor) / Bremner, Andrew (Advisor) / Childress, Nancy (Committee member) / Fishel, Susanna (Committee member) / Kaliszewski, Steven (Committee member) / Arizona State University (Publisher)
Subject Mathematics
Type Doctoral Dissertation
Extent 2610 pages
Language English
Copyright
Note Doctoral Dissertation Mathematics 2019
Collaborating Institutions Graduate College / ASU Library
Additional Formats MODS / OAI Dublin Core / RIS


This content is under embargo until May 01, 2021

  Full Text
6.8 MB application/pdf
  • Download restricted
Download Count: 0

Description Dissertation/Thesis