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20G35 Group theory and generalizations -- Linear algebraic groups and related topics -- Linear algebraic groups over adèles and other rings and schemes

11R56 Number theory -- Algebraic number theory: global fields -- Adèle rings and groups

43A70 Abstract harmonic analysis -- Abstract harmonic analysis -- Analysis on specific locally compact and other abelian groups En-ligne: Numir | Springerlink | Zentralblatt | MathSciNet

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This very influential work only existed up to now as mimeographed lecture notes, not easily available from the Institute for Advanced Study, and it is a very welcome move to have it reprinted in book form. After the introduction of idèles in number theory by Chevalley, A. Weil had already seen in 1938 that, more generally, adèles could also be used in that theory, and in 1957, T. Ono had made a first study of adelized algebraic groups. Then, in 1959, Tamagawa discovered what are now called Tamagawa measures and their relation to Siegel's work on quadratic forms, but his paper on this subject was only published in 1966 [T. Tamagawa, Proc. Sympos. Pure Math. 9, 113–121 (1966; Zbl 0178.23801)]. A. Weil, who had seen Tamagawa's manuscript, at once realized its importance, and made it a subject of lectures he gave in 1959–60 (and which are reproduced in this book), enriched by many original viewpoints and results, giving the impetus to the modern theory of arithmetic groups. (Zentralblatt)

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