Browsing by Subject "Algebraic spaces"
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Item Auxiliary polynomials and height functions(2007) Samuels, Charles Lloyd, 1980-; Vaaler, Jeffrey D.We establish two new results in this dissertation. Recent theorems of Dubickas and Mossinghoff use auxiliary polynomials to give lower bounds on the Weil height of an algebraic number [alpha] under certain assumptions on [alpha]. We prove a theorem which introduces an auxiliary polynomial for giving lower bounds on the height of any algebraic number. In particular, we prove the following theorem. [Mathematical equations]