Minimal Determinants and Lattice Inequalities |
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Authors: | Schnell Uwe |
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Affiliation: | Mathematisches Institut, Universität Siegen D-5900 Siegen, Germany |
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Abstract: | Some results of P. McMullen on determinants of sublattices ofZd induced by rational subspaces are generalized to arbitrarylattices. As an application, we obtain an equality for the minimaldeterminants introduced by J. M. Wills, namely Dt(L) = Dd(L)Dd1((L*).Using an inequality of Lagarias, Lenstra and Schnorr, we generalizetwo isoperimetric inequalities withlattice constraints by Bokowski,Hadwiger and Wills, and Hadwiger, respectively, to arbitrarylattices. |
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