New bounds in some transference theorems in the geometry of numbers

@article{Banaszczyk1993NewBI,
  title={New bounds in some transference theorems in the geometry of numbers},
  author={W. Banaszczyk},
  journal={Mathematische Annalen},
  year={1993},
  volume={296},
  pages={625-635}
}
The aim of this paper is to give new bounds in certain inequalities concerning mutually reciprocal lattices in R". To formulate the problem, we have to introduce some notation and terminology. We shall treat IR" as an n-dimensional euclidean space with the norm II II and metric d. The inner product of vectors u, v will be denoted by uv; we shall usually write u 2 instead of uu. The closed and open unit balls in F," will be denoted by B, and B'., respectively. If A c IR ", then span A and A z… Expand
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