Geodesic
Deformations of Diophantine systems for quadratic forms of the cubic lattices
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 18, Tome 286 (2002), pp. 5-35

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The method of deformation is applied to quadratic Diophantine systems determined by the cubic lattices $\mathbb Z^n$. 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. 
@article{ZNSL_2002_286_a0,
     author = {N. V. Budarina},
     title = {Deformations of {Diophantine} systems for quadratic forms of the cubic lattices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--35},
     publisher = {mathdoc},
     volume = {286},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_286_a0/}
}
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N. V. Budarina. Deformations of Diophantine systems for quadratic forms of the cubic lattices. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 18, Tome 286 (2002), pp. 5-35. http://geodesic.mathdoc.fr/item/ZNSL_2002_286_a0/