Geodesic
Local volume computations in the Siegel–Tamagawa formula
Sbornik. Mathematics, Tome 66 (1990) no. 2, pp. 447-460 
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/
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     author = {V. E. Voskresenskii},
     title = {Local volume computations in the {Siegel{\textendash}Tamagawa} formula},
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     pages = {447--460},
     year = {1990},
     volume = {66},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1990_66_2_a9/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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