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Über den Satz von Weil-Cartier

On the Weil-Cartier theorem

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It is shown that the theorem ofWeil-Cartier ([10, Th. 5], [4, Th. 3]) is connected with a homomorphism of groups of unitary operators. The existence proof for this homomorphism is based on simple results in harmonic analysis and on an extension property of the Schwartz-Bruhat functions. Some applications are given, including a result ofIgusa's [6, Th. 3] and the reciprocity formula ofKrazer-Siegel [9, Th. 2]. An outline of the proof has been given in [8].

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  1. Barner, K.: Zur Reziprozität quadratischer Charaktersummen in algebraischen Zahlkörpern. Mh. Math.71, 369–384 (1967).

    Article  MathSciNet  MATH  Google Scholar 

  2. Bourbaki, N.: Théories Spectrales, Chaps. 1, 2: Algèbres Normées, Groupes Localement Compacts Commutatifs (Éléments de Mathématique, Fasc. XXXII). Paris: Hermann. 1967.

    MATH  Google Scholar 

  3. Bruhat, F.: Distributions sur un groupe localement compact et applications à l'étude des représentations des groupesp-adiques. Bull. Soc. Math. France89, 43–75 (1961).

    MathSciNet  MATH  Google Scholar 

  4. Cartier, P.: Über einige Integralformeln in der Theorie der quadratischen Formen. Math. Z.84, 93–100 (1964).

    Article  MathSciNet  MATH  Google Scholar 

  5. Hochschild, G.: The Structure of Lie Groups. San Francisco-London-Amsterdam: Holden-Day. 1965.

    MATH  Google Scholar 

  6. Igusa, J.: Harmonic analysis and theta-functions. Acta Math.120, 187–222 (1968).

    Article  MathSciNet  MATH  Google Scholar 

  7. Reiter, H.: Classical Harmonic Analysis and Locally Compact Groups. Oxford: Oxford University Press. 1968.

    MATH  Google Scholar 

  8. Reiter, H.: Sur le théorème de Weil-Cartier. C. R. Acad. Sci. Paris, Série A,284, 951–954 (1977).

    MathSciNet  MATH  Google Scholar 

  9. Siegel, C. L.: Über das quadratische Reziprozitätsgesetz in algebraischen Zahlkörpern. Nachr. Ges. Wiss. Göttingen, Math.-Phys. Kl., Nr.1, 1–16 (1960)=Gesammelte AbhandlungenIII, 334–349. Berlin-Heidel-berg-New York: Springer. 1966.

  10. Weil, A.: Sur certains groupes d'opérateurs unitaires. Acta Math.111, 143–211 (1964).

    Article  MathSciNet  MATH  Google Scholar 

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Reiter, H. Über den Satz von Weil-Cartier. Monatsh Math 86, 13–62 (1978).

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