The Height In Terms Of The Normalizer Of A Stabilizer.

Book Description:

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.