Abstract:
The author studies the local factors in Siegel–Tamagawa products and the products themselves. To do this he examines integral structures in linear algebraic groups and gives a construction of an invariant density which induces the canonical Haar measure at $p$-adic places. The local volume computations reduce to the study of the factors at places of bad reduction. An exact expression is obtained for the weight of the genus of a unimodular lattice.
Bibliography: 13 titles.
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