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- W2021586148 abstract "Abstract Let 1 ≤ M ≤ N − 1 be integers and K be a convex, symmetric set in Euclidean N -space. Associated with K and M , Mahler identified the M th compound body of K, (K) m , in Euclidean ( M N )-space. The compound body (K) M is describable as the convex hull of a certain subset of the Grassmann manifold in Euclidean ( M N )-space determined by K and M . The sets K and (K) M are related by a number of well-known inequalities due to Mahler. Here we generalize this theory to the geometry of numbers over the adèle ring of a number field and prove theorems which compare an adelic set with its adelic compound body. In addition, we include a comparison of the adelic compound body with the adelic polar body and prove an adelic general transfer principle which has implications to Diophantine approximation over number fields." @default.
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- W2021586148 date "1993-10-01" @default.
- W2021586148 modified "2023-09-25" @default.
- W2021586148 title "On Mahler's compound bodies" @default.
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- W2021586148 doi "https://doi.org/10.1017/s144678870003202x" @default.
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