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An Extreme Duodenary Form

Published online by Cambridge University Press:  20 November 2018

H. S. M. Coxeter  and
J. A. Todd
H. S. M. Coxeter
Affiliation:
University of Toronto
J. A. Todd
Affiliation:
University of Cambridge
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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

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 5 , 1953 , pp. 384 - 392
Copyright
Copyright © Canadian Mathematical Society 1953

References

1. Coxeter, H. S. M., Extreme forms, Can. J. Math., 8 (1951), 391–441.Google Scholar
2. Hamill, C. M., On a finite group of order 6,531,840, Proc. London Math. Sotv(2), 52 (1951), 401–454.Google Scholar
3. Hartley, E. M., A sextic primal in five dimensions, Proc. Cambridge Phil. Soc, 46 (1950), 91–105.Google Scholar
4. Ko, Chao, On the positive definite quadratic forms with determinant unity, Acta Arithmetica, 5(1939), 79–85.Google Scholar
5. Korkine, A. and Zolotareff, G., Sur les formes quadratiques, Math. Ann., 6 (1873), 366–389.Google Scholar
6. Mitchell, H. H., Determination of all primitive collineation groups in more than four variables which contain homologies, Amer. J. Math., 86 (1914), 1–12.Google Scholar
7. Shephard, G. C., Regular complex polytopes, Proc. London Math. Soc. (3), 2 (1952), 82–97.Google Scholar
7a. Shephard, G. C., Unitary groups generated by reflections. Can. J. Math., 5 (1953), 364–383.Google Scholar
8. Todd, J. A., The invariants of a finite collineation group in five dimensions, Proc. Cambridge Phil. Soc, 46 (1950), 73–90.Google Scholar
9. Todd, J. A., The characters of a collineation group in five dimensions, Proc. Royal Soc. London, A, 200 (1950), 320–336.Google Scholar
10. Voronï, G., Sur quelques propriétés des formes quadratiques positives parfaites., J. reïne angew. Math., 188 (1907), 97–178.Google Scholar
11. Weyl, H., Gruppentheorie und Quantenmechanik (Leipzig, 1928).Google Scholar
12. Weyl, H., The theory of groups and quantum mechanics (New York, 1931).Google Scholar