2:00 pm Thursday, September 12, 2013
Algebra, Number Theory, and Combinatorics: Structure theorems for multiplicative groups of algebraic numbers by Jeff Vaaler (University of Texas at Austin) in RLM 9.166
Let K be an algebraic extension of the field Q of rational numbers. Write F(K) for the multiplicative group of K modulo its torsion subgroup, E(K) for the rational vector space generated by F(K), and X(K) for the closure of E(K) with respect to the metric induced in E(K) by the Weil height. We will describe some recent results about the algebraic and topological structure of these objects. The space X(K) is a real Banach space, and if K is a finite extension of Q, we describe a special Schauder basis in X(K). Using this Schauder basis we prove a new, seemingly elementary, result about points in E(K) with small height. This is joint work with R. Grizzard. Submitted by
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