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An Extreme Duodenary Form

  • H. S. M. Coxeter (a1) and J. A. Todd (a2)

Extract

Let f(x1, … , xn) be a positive definite quadratic form of determinant Δ; let M be its minimum value for integers x1, … , xn not all zero; and let 2s be the number of times this minimum is attained, i.e., the number of solutions of the Diophantine equation

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References

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1. Coxeter, H. S. M., Extreme forms, Can. J. Math., 8 (1951), 391441.
2. Hamill, C. M., On a finite group of order 6,531,840, Proc. London Math. Sotv(2), 52 (1951), 401454.
3. Hartley, E. M., A sextic primal in five dimensions, Proc. Cambridge Phil. Soc, 46 (1950), 91105.
4. Ko, Chao, On the positive definite quadratic forms with determinant unity, Acta Arithmetica, 5(1939), 7985.
5. Korkine, A. and Zolotareff, G., Sur les formes quadratiques, Math. Ann., 6 (1873), 366389.
6. Mitchell, H. H., Determination of all primitive collineation groups in more than four variables which contain homologies, Amer. J. Math., 86 (1914), 112.
7. Shephard, G. C., Regular complex polytopes, Proc. London Math. Soc. (3), 2 (1952), 8297.
7a. Shephard, G. C., Unitary groups generated by reflections. Can. J. Math., 5 (1953), 364383.
8. Todd, J. A., The invariants of a finite collineation group in five dimensions, Proc. Cambridge Phil. Soc, 46 (1950), 7390.
9. Todd, J. A., The characters of a collineation group in five dimensions, Proc. Royal Soc. London, A, 200 (1950), 320336.
10. Voronï, G., Sur quelques propriétés des formes quadratiques positives parfaites., J. reïne angew. Math., 188 (1907), 97178.
11. Weyl, H., Gruppentheorie und Quantenmechanik (Leipzig, 1928).
12. Weyl, H., The theory of groups and quantum mechanics (New York, 1931).
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