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On the Arithmetic of Pfaffians1)
Published online by Cambridge University Press: 22 January 2016
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In this paper, we shall supply proofs to the results announced in [2], pp. 74-75: we shall prove the Siegel formula for the Pfaffian of degree n over an algebraic number field and also determine the zeta function of the Pfaffian. In the appendix, we shall briefly discuss the non-split case where the Pfaffian is replaced by the norm form of the simple Jordan algebra of quaternionic hermitian matrices of degree n.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1972
Footnotes
1)
This work was partially supported by the National Science Foundation.
References
[1]
Chevalley, C., The construction and study of certain important algebras, Pub. Math. Soc. Japan, 1 (1955).Google Scholar
[2]
Igusa, J., Some observations on the Siegel formula, Rice Univ. Studies, 56 (1970), 67–75.Google Scholar
[3]
Igusa, J., On certain representations of semi-simple algebraic groups and the arithmetic of the corresponding invariants (1), Inventiones Math., 12 (1971), 62–94.Google Scholar
[5]
Mars, J. G. M., Les nombres de Tamagawa de certains groupes exceptionels, Bull. Soc. Math. France, 94 (1966), 97–140.Google Scholar
[8]
Weil, A., Sur certain groupes d’opérateurs unitaires, Acta Math., 111 (1964), 143–211.Google Scholar
[9]
Weil, A., Sur la formule de Siegel dans la theorie des groupes classiques, Acta Math., 113 (1965), 1–87.Google Scholar
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