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Deformations of Diophantine systems for quadratic forms of cubic lattices. (English. Russian original) Zbl 1077.11025
J. Math. Sci., New York 122, No. 6, 3583-3599 (2004); translation from Zap. Nauchn. Semin. POMI 286, 5-35 (2002).
Summary: The method of deformation is applied to quadratic Diophantine systems determined by cubic lattices \(\mathbb Z\). The method allows one to find from known formulas for the number of representations of quadratic forms by a genus of forms an infinite set of other formulas for equations and systems with smaller number of variables.

MSC:
11E12 Quadratic forms over global rings and fields
11D85 Representation problems
11E20 General ternary and quaternary quadratic forms; forms of more than two variables
11E25 Sums of squares and representations by other particular quadratic forms
11H55 Quadratic forms (reduction theory, extreme forms, etc.)
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