On metric Diophantine approximation in matrices and Lie groups

• We study the Diophantine exponent of analytic submanifolds of m x n real matrices, answering questions of Beresnevich, Kleinbock, and Margulis. We identify a family of algebraic obstructions to the extremality of such a submanifold, and give a formula for the exponent when the submanifold is algebraic and defined over Q. We then apply these results to the determination of the Diophantine exponent of rational nilpotent Lie groups.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Publication and Content Type

ref (subject category)

art (subject category)