Takao Watanabe: Fundamental Hermite constants of linear algebraic groups


Submission: 2003, Jan 9

As an analogue of Hermite-Rankin's constant, we introduce a constant attached to a pair of a connected reductive algebraic group $G$ and its maximal parabolic subgroup $Q$ both defined over a global field. This constant measures a distribution of rational points of a flag variety $G/Q$ with small height. Though we use adelic language, the definition of this constant is given as a natural generalization of Hermite's constant. Some results on Hermite-Rankin's constant, e.g., Rankin's inequality, Minkowski-Hlawka's lower bound, are generalized to this constant.

2000 Mathematics Subject Classification: 11R56, 11G35, 14G25

Keywords and Phrases: Hermite constant, reduction theory, flag variety

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