Geodesic
Some Results on Totally Isotropic Subspaces and Five-Dimensional Quadratic Forms Over GF(q)
Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 271-275

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Cordes, Craig M. Some Results on Totally Isotropic Subspaces and Five-Dimensional Quadratic Forms Over GF(q). Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 271-275. doi: 10.4153/CJM-1975-033-8
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[1] 1. Artin, E., Geometric algebra (Interscience, New York, 1957). Google Scholar

[2] 2. Couvillon, L., Partitionings by means of maximal isotropic spaces, Ph.D. Thesis, Louisiana State University, 1971. Google Scholar

[3] 3. Dieudonné, J., La géométrie des groupes classiques (Springer-Verlag, Berlin, 1971). Google Scholar

[4] 4. O'Meara, O. T., Introduction to quadratic forms (Springer-Verlag, New York, 1963). Google Scholar

[5] 5. Pall, G., Partitioning by means of maximal isotropic subspaces, Linear Algebra and Appl. 5 (1972), 173–180. Google Scholar

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