Hostname: page-component-6dbcb7884d-4vmf6 Total loading time: 0 Render date: 2025-02-13T21:12:58.597Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Arithmetic of Pfaffians1)

Published online by Cambridge University Press:  22 January 2016

Jun-Ichi Igusa
Jun-Ichi Igusa*
Affiliation:
The Johns Hopkins University, Baltimore, Maryland 21218
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 47 , September 1972 , pp. 169 - 198
Copyright
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
[4] Lang, S., Diophantine geometry, Interscience Pub., 11 (1962).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
[6] Siegel, C. L., Gesammelte Abhandlungen I-III, Springer (1966).Google Scholar
[7] Weil, A., Adels and algebraic groups, Lecture Note, Princeton (1961).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