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. / text
Identifer | oai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/3846 |
Date | 29 August 2008 |
Creators | Garza, John Matthew, 1975- |
Source Sets | University of Texas |
Language | English |
Detected Language | English |
Type | Thesis |
Format | electronic |
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. |
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