ERC Research Period on Diophantine Geometry
timetable:
Thu 11 Oct, 10:30 - 11:10, Sala Conferenze Centro De Giorgi
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Heights on Groups and Small Multiplicative Dependencies (40')
speaker: Jeff Vaaler (University of Texas at Austin)abstract: Let G denote the multiplicative group of nonzero algebraic numbers modulo its torsion subgroup. We will describe a generalization of the absolute logarithmic Weil height from elements of G to finitely generated subgroups of G. This height is also equal to the volume of a related convex symmetric subset of a Euclidean space. The height-volume connection leads to a bound on the norm of integer vectors that give multiplicative dependencies among finite sets of algebraic numbers. The bound we obtain is independent of number fields that contain the finite set of algebraic numbers.
timetable:
Thu 11 Oct, 10:30 - 11:10, Sala Conferenze Centro De Giorgi
<< Go back