The height in terms of the normalizer of a stabilizer
| dc.contributor.advisor | Vaaler, Jeffrey D. | en |
| dc.creator | Garza, John Matthew, 1975- | en |
| dc.date.accessioned | 2008-08-29T00:14:14Z | en |
| dc.date.available | 2008-08-29T00:14:14Z | en |
| dc.date.issued | 2008-05 | en |
| dc.description | text | en |
| dc.description.abstract | This dissertation is about the Weil height of algebraic numbers and the Mahler measure of polynomials in one variable. We investigate connections between the normalizer of a stabilizer and lower bounds for the Weil height of algebraic numbers. In the Archimedean case we extend a result of Schinzel [Sch73] and in the non-archimedean case we establish a result related to work of Amoroso and Dvornicich [Am00a]. We establish that amongst all polynomials in Z[x] whose splitting fields are contained in dihedral Galois extensions of the rationals, x³-x-1, attains the lowest Mahler measure different from 1. | en |
| dc.description.department | Mathematics | en |
| dc.format.medium | electronic | en |
| dc.identifier | b70654670 | en |
| dc.identifier.oclc | 241300502 | en |
| dc.identifier.uri | http://hdl.handle.net/2152/3846 | en |
| dc.language.iso | eng | en |
| dc.rights | Copyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works. | en |
| dc.subject.lcsh | Algebra | en |
| dc.subject.lcsh | Polynomials | en |
| dc.title | The height in terms of the normalizer of a stabilizer | en |
| dc.type.genre | Thesis | en |
| thesis.degree.department | Mathematics | en |
| thesis.degree.discipline | Mathematics | en |
| thesis.degree.grantor | The University of Texas at Austin | en |
| thesis.degree.level | Doctoral | en |
| thesis.degree.name | Doctor of Philosophy | en |