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Some Results on Totally Isotropic Subspaces and Five-Dimensional Quadratic Forms Over GF(q)

Published online by Cambridge University Press:  20 November 2018

Craig M. Cordes
Craig M. Cordes*
Affiliation:
Louisiana State University, Baton Rouge, Louisiana
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In [5] Pall denned a partitioning of a quadratic space over a field of characteristic not 2 to be a collection of disjoint (except for ﹛0﹜ ) maximal totally isotropic subspaces whose union formed the set of isotropic vectors. Clearly isometric quadratic spaces simultaneously do or do not have partitionings. Pall exhibited the existence of partitionings for the spaces associated with

over formally real fields for n = 1, 2, 4, 8 and over Z/(p), p prime, for n = 1, 2. Using the latter, he was able to find a new proof for Jacobi's formula for the number of representations of a positive integer as the sum of four integral squares.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 2 , 01 April 1975 , pp. 271 - 275
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Artin, E., Geometric algebra (Interscience, New York, 1957).Google Scholar
2. Couvillon, L., Partitionings by means of maximal isotropic spaces, Ph.D. Thesis, Louisiana State University, 1971.Google Scholar
3. Dieudonné, J., La géométrie des groupes classiques (Springer-Verlag, Berlin, 1971).Google Scholar
4. O'Meara, O. T., Introduction to quadratic forms (Springer-Verlag, New York, 1963).Google Scholar
5. Pall, G., Partitioning by means of maximal isotropic subspaces, Linear Algebra and Appl. 5 (1972), 173–180.Google Scholar