# zbMATH — the first resource for mathematics

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.)
Full Text: