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The theory of hermite-Minkowski reduction of positive definite quadratic forms

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Literature cited

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    H. Minkowski, “Diskontinuitätsbereich für arithmetische Aequivalenz,” Ges. Abh.,2, 53–103 (1911).

  2. 2.

    B. N. Delone, “The geometry of positive definite quadratic forms,” Usp. Matem. Nauk, No. 3, 16–62 (1937); No. 4, 102–164 (1938).

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    B. L. van der Waerden, “Die Reduktionstheorie der quadratischen Formen,” Acta Mathem.,96, 265–309 (1956);98, 3–4 (1957).

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    B. A. Venkov, “The reduction of positive definite quadratic forms,” Izv. Akad. Nauk SSSR Ser. Matem.,4, 37–52 (1940).

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    G. F. Voronoi, “Some properties of positive definite perfect quadratic forms,” in: Collected Works [in Russian], Vol. 2 (1952), pp. 171–238.

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    S. S. Ryshkov, “The theory of reduction of positive definite quadratic forms in five variables,” in: Proc. of the 2nd Tiraspol Symposium on General Topology and Its Applications, Kishinev [in Russian] (1969), pp. 65–67.

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    H. Minkowski, “Sur la reduction des formes quadratiques positives quaternaires,” Ges. Abh.,1, 145–148 (1911).

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    H. Minkowski, “Über positive quadratische Formen,” Ges. Abh.,1, 149–156 (1911).

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    H. Minkowski, “Zur Theorie der positiven quadratischen Formen,” Ges. Abh.1, 212–218 (1911).

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    Ch. Hermite, “Lettres sur differents objects de la theorie des nombres,” in: Oeuvres, Vol. 1, pp. 100–163.

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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 33, pp. 37–64, 1973.

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Ryshkov, S.S. The theory of hermite-Minkowski reduction of positive definite quadratic forms. J Math Sci 6, 651–671 (1976). https://doi.org/10.1007/BF01092510

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Keywords

  • Quadratic Form
  • Positive Definite Quadratic Form