The height in terms of the normalizer of a stabilizer

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Title: The height in terms of the normalizer of a stabilizer
Author: Garza, John Matthew, 1975-
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 .
URI: http : / /hdl .handle .net /2152 /3846
Date: 2008-08-29

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The height in terms of the normalizer of a stabilizer. Doctoral dissertation, The University of Texas at Austin. Available electronically from http : / /hdl .handle .net /2152 /3846 .

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