Geodesic
Explicit duality formulas for symplectic and orthogonal Hecke operators on theta-series of positive quadratic forms
Sbornik. Mathematics, Tome 58 (1987) no. 2, pp. 417-434

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The Rallis mapping is used to obtain commutation formulas for the Hecke operators of the symplectic and orthogonal groups on the space of theta-series. These formulas are applied to the multiplicative arithmetic of representations of quadratic forms by forms. Bibliography: 15 titles. 
@article{SM_1987_58_2_a7,
     author = {V. G. Zhuravlev},
     title = {Explicit duality formulas for symplectic and orthogonal {Hecke} operators on theta-series of positive quadratic forms},
     journal = {Sbornik. Mathematics},
     pages = {417--434},
     publisher = {mathdoc},
     volume = {58},
     number = {2},
     year = {1987},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1987_58_2_a7/}
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V. G. Zhuravlev. Explicit duality formulas for symplectic and orthogonal Hecke operators on theta-series of positive quadratic forms. Sbornik. Mathematics, Tome 58 (1987) no. 2, pp. 417-434. http://geodesic.mathdoc.fr/item/SM_1987_58_2_a7/