Budarina, N. V. Deformations of Diophantine systems for quadratic forms of the root lattices \(A_n\). (Russian, English) Zbl 1076.11026 Zap. Nauchn. Semin. POMI 314, 5-14, 285 (2004); translation in J. Math. Sci., New York 133, No. 6, 1605-1610 (2006). The matrix equation \(Q[X] = {^tT}QT = A\) is studied, where \(Q\) and \(A\) are positive definite symmetric integral matrices of order \(n\) and \(m\), respectively, and \(T\) ranges over the set of \(n\times m\) integer matrices. When \(A = A' \oplus A''\), where the summands have squarefree and coprime determinants, a formula is found for the weighted average of representations of \(A''\) by a suitable quadratic form \(Q'\). This computation depends on the approach due to V. G. Zhuravlev [Algebra Anal. 8 , No. 1, 21–112 (1996; Zbl 0860.11018)]. Two concrete numerical cases are considered in detail. Reviewer: K. Szymiczek (Katowice) 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 Keywords:embeddings of lattices; weight of representations PDF BibTeX XML Cite \textit{N. V. Budarina}, Zap. Nauchn. Semin. POMI 314, 5--14, 285 (2004; Zbl 1076.11026); translation in J. Math. Sci., New York 133, No. 6, 1605--1610 (2006) Full Text: EuDML