Abstract
For a generating Dirichlet vector series with coefficients equal to the number of representations of a quadratic form by another one we abtain a decomposition into the product of a finite number of Dirichlet L-functions and an infinite number of matrix polynomials. The coefficients of the polynomials are the Eichler-Brandt matrices of the basis double cosets of the local orthogonal Hecke rings.
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