The Construction of Perfect and Extreme Forms
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 147-158

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Let be a positive quadratic form of determinant D, and let M be the minimum of f(x) for integral x ≠ 0. Then f(x) assumes the value M for a finite number of integral vectors x = ±mk (k = 1 , ... , s) called the minimal vectors.
Scott, P. R. The Construction of Perfect and Extreme Forms. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 147-158. doi: 10.4153/CJM-1966-019-x
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[1] 1. Barnes, E. S., The complete enumeration of extreme senary forms, Phil. Trans. Roy. Soc., (A) 249 (1957), 461–506 Google Scholar

[2] 2. Barnes, E. S., The construction of perfect and extreme forms I and II, Acta Arith., 5 (1958), 57–79; 5 (1959), 205-222. Google Scholar

[3] 3. Barnes, E. S. and Wall, G. E., Some extreme forms defined in terms of abelian groups, J. Austral. Math. Soc, 1 (1959), 47–63. Google Scholar

[4] 4. Coxeter, H. S. M., Extreme forms, Can. J. Math., 3 (1951), 391–441. Google Scholar

[5] 5. Coxeter, H. S. M. and Todd, J. A., An extreme duodenary form, Can. J. Math., 5 (1951), 384–392. Google Scholar

[6] 6. Korkine, A. and Zolotareff, G., Sur les formes quadratiques positives, Math. Ann., 11 (1877), 242–392. Google Scholar

[7] 7. Minkowski, H., Diskontinuitätsbereich für arithmetische Äquivalenz, J. Reine Angew. Math., 129 (1905), 220–274. Google Scholar

[8] 8. Mordell, L. J., Observation on the minimum of a positive quadratic form in eight variables, J. London Math. Soc, 19 (1944), 3–6. Google Scholar

[9] 9. Scott, P. R., On perfect and extreme forms, J. Austral. Math. Soc, 4 (1964), 56–77. Google Scholar

[10] 10. Voronoi, G., Sur quelques propriétés des formes quadratiques positives parfaites, J. Reine Angew. Math., 138 (1908), 97–178. Google Scholar

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