Abstract
The aim of this chapter is to prove certain inequalities which will allow us to get lower bounds (and sometimes upper bounds) for lattice constants (defined in Section 2.5) for some important subsets of ℝn. Though our aim is to study balls (one says traditionally “spheres”) centred at the origin, some more general bodies are dealt with, either because it seems useful to consider there more general questions, or in order to give applications of spheres to various questions in the geometry of numbers.
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© 2003 Springer-Verlag Berlin Heidelberg
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Martinet, J. (2003). Geometric Inequalities. In: Perfect Lattices in Euclidean Spaces. Grundlehren der mathematischen Wissenschaften, vol 327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05167-2_2
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DOI: https://doi.org/10.1007/978-3-662-05167-2_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07921-4
Online ISBN: 978-3-662-05167-2
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