Geodesic
Euler decompositions for theta-series of even quadratic forms
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 12, Tome 212 (1994), pp. 97-113

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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. Bibliography: 3 titles. 
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     author = {V. G. Zhuravlev},
     title = {Euler decompositions for theta-series of even quadratic forms},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {97--113},
     publisher = {mathdoc},
     volume = {212},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_212_a6/}
}
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V. G. Zhuravlev. Euler decompositions for theta-series of even quadratic forms. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 12, Tome 212 (1994), pp. 97-113. http://geodesic.mathdoc.fr/item/ZNSL_1994_212_a6/