Geodesic
Local volume computations in the Siegel--Tamagawa formula
Sbornik. Mathematics, Tome 66 (1990) no. 2, pp. 447-460

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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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     author = {V. E. Voskresenskii},
     title = {Local volume computations in the {Siegel--Tamagawa} formula},
     journal = {Sbornik. Mathematics},
     pages = {447--460},
     publisher = {mathdoc},
     volume = {66},
     number = {2},
     year = {1990},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1990_66_2_a9/}
}
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V. E. Voskresenskii. Local volume computations in the Siegel--Tamagawa formula. Sbornik. Mathematics, Tome 66 (1990) no. 2, pp. 447-460. http://geodesic.mathdoc.fr/item/SM_1990_66_2_a9/