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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A mean value formula for the spin group
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by Lawrence Verner PDF
Proc. Amer. Math. Soc. 50 (1975), 68-72 Request permission

Abstract:

An adelic mean value formula is proved for two-connected algebraic homogeneous spaces, generalizing Siegel’s formula in the geometry of numbers. The case of the spin group acting on the generalized sphere furnishes an example. The procedure consists in applying Galois cohomological techniques to the method of Ono.
References
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  • Martin Kneser, Hasse principle for $H^{1}$ of simply connected groups, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965) Amer. Math. Soc., Providence, R.I., 1966, pp. 159–163. MR 0220736
  • Takashi Ono, A mean value theorem in adele geometry, J. Math. Soc. Japan 20 (1968), 275–288. MR 230726, DOI 10.2969/jmsj/02010275
  • Carl Ludwig Siegel, A mean value theorem in geometry of numbers, Ann. of Math. (2) 46 (1945), 340–347. MR 12093, DOI 10.2307/1969027
  • A. Weil, Adeles and algebraic groups, Institute for Advanced Study, Princeton, N. J., 1966. MR 6, 257.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 50 (1975), 68-72
  • MSC: Primary 10C30; Secondary 12A85
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0382168-4
  • MathSciNet review: 0382168