2012/11/21 by Vaaler, Jeffrey D.
#11J25 #11R04 #46B04 #FOS: Mathematics #Functional Analysis (math.FA) #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1211.5066
We generalize the absolute logarithmic Weil height from elements of the multiplicative group of algebraic numbers modulo torsion, to finitely generated subgoups. The height of a finitely generated subgroup is shown to equal the volume of a certain naturally occurring, convex, symmetric subset of Euclidean space. This connection leads to a bound on the norm of integer vectors that give multiplicative dependencies among finite sets of algebraic numbers.