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On perfect and extreme forms

Published online by Cambridge University Press:  09 April 2009

P. R. Scott
P. R. Scott
Affiliation:
University of Adelaide, South Australia.
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Let (х) = (x1, x2, … xn) = Σi Σiaij, xixf (aij = aij) be a positive quadratic form with determinant D, and let M be the minimum of for integral x ≠ 0. Then attains the value M for a finite number of integral x = ±mk ( k = 1, …, s) called its minimal vectors.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 4 , Issue 1 , February 1964 , pp. 56 - 77
Copyright
Copyright © Australian Mathematical Society 1964

References

[1]Barnes, E. S., Criteria for extreme forms, This Journal 1 (1959), 17–20.Google Scholar
[2]Barnes, E. S., The complete enumeration of extreme senary forms, Phil. Trans. Roy. Soc. London (A) 249 (1957), 461–506.Google Scholar
[3]Barnes, E. S., The construction of perfect and extreme forms I and II, Acta Arith. 5 (1958), 57–79; 5 (1959), 205–222.CrossRefGoogle Scholar
[4]Barnes, E. S. and Wall, G. E., Some extreme forms defined in terms of abelian groups, This Journal 1 (1959), 47–63.Google Scholar
[5]Chaundy, T. W., The arithmetic minima of positive quadratic forms, Quart. J. Math. (Oxford) 17 (1946), 166–192.Google Scholar
[6]Coxeter, H. S. M., Extreme forms, Canad. J. Math. 3 (1951), 391–441.CrossRefGoogle Scholar
[7]Coxeter, H. S. M. and Todd, J. A., An extreme duodenary form, Canad. J. Math. 5 (1951), 384–392.CrossRefGoogle Scholar
[8]Korkine, A. and Zolotareff, G., Sur les formes quadratiques positives, Math. Ann. 11 (1877), 242–392.CrossRefGoogle Scholar
[9]Voronoi, G., Sur quelques propriétés des formes quadratiques positives parfaites, J. reine angew. Math. 133 (1908), 97–178.CrossRefGoogle Scholar
[10]Wall, G. E., On the Clifford collineation, transform and similarity groups (IV), Nagoya Math. J. 21 (1962), 199–222.Google Scholar