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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

A Siegel formula for orthogonal groups over a function field


Author: Stephen J. Haris
Journal: Trans. Amer. Math. Soc. 190 (1974), 223-231
MSC: Primary 10C15; Secondary 12A85
DOI: https://doi.org/10.1090/S0002-9947-1974-0349584-1
MathSciNet review: 0349584
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Abstract | References | Similar Articles | Additional Information

Abstract: We obtain a Siegel formula for a quadratic form over a function field, by establishing the convergence of the corresponding Eisenstein-Siegel series directly, then via the Hasse principle, that of the associated Poisson formula.


References [Enhancements On Off] (What's this?)

  • [1] A. Borel and T. Springer, Rationality properties of linear algebraic groups, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965), Amer. Math. Soc., Providence, R. I., 1966, pp. 26-32. MR 34 #5823. MR 0205998 (34:5823)
  • [2] J. Igusa, On certain representations of semi-simple algebraic groups and the arithmetic of the corresponding invariants. I, Invent. Math. 12 (1971), 62-94. MR 45 #6823. MR 0297771 (45:6823)
  • [3] -, On the arithmetic of Pfaffions, Nagoya Math. J. 47 (1972), 169-198. MR 0376623 (51:12798)
  • [4] A. Weil, Basic number theory, Die Grundlehren der math. Wissenschaften, Band 144, Springer-Verlag, New York, 1967. MR 38 #3244. MR 0234930 (38:3244)
  • [5] -, Adeles and algebraic groups, Inst. for Advanced Study, Princeton, N. J., 1961.
  • [6] -, Sur certains groupes d'opérateurs unitaires, Acta Math. 111 (1964), 143-211. MR 29 #2324. MR 0165033 (29:2324)
  • [7] -, Sur la formule de Siegel dans la théorie des groupes classiques, Acta Math. 113 (1965), 1-87. MR 36 #6421. MR 0223373 (36:6421)

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DOI: https://doi.org/10.1090/S0002-9947-1974-0349584-1
Article copyright: © Copyright 1974 American Mathematical Society

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