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Witt's Theorem for Symplectic Modular Forms1

Published online by Cambridge University Press:  09 April 2009

D. G. James
D. G. James
Affiliation:
The Pennsylvania State University
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Let L denote a free Z-module of rank 2n and Φ an alternating bilinear mapping from L×L into the rational integers Z. Writing α · β for Φ(α, β), where α, β ∈ L, we have We shall assume that Φ is non-singular and unimodular (see Bourbaki [1]). L is now a (symplectic) lattice.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 9 , Issue 3-4 , May 1969 , pp. 409 - 414
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Bourbaki, , Algèbre ch. 9, (Hermann, Paris, 1959).Google Scholar
[2]Dieudonné, J., La géométrie des groupes classiques, (Springer-Verlag, Berlin, 1963).CrossRefGoogle Scholar
[3]James, D. G., ‘Integral invariants for vectors over local fields’, Pac. J. Math. 15 (1965), 905–916.CrossRefGoogle Scholar
[4]James, D. G., ‘Transitivity in integral symplectic forms’, J. Aust. Math. Soc. 8 (1968), 43–48.CrossRefGoogle Scholar
[5]O'Meara, O. T., ‘Quadratic forms over local fields’, Amer. J. Math. 77 (1955), 87–116.CrossRefGoogle Scholar
[6]Witt, E., ‘Theorie der quadratischen Formen in beliebigen Körpern’, J. reine angew. Math. 176 (1937), 31–44.CrossRefGoogle Scholar