Geodesic
Hecke rings for a~covering of the symplectic group
Sbornik. Mathematics, Tome 49 (1984) no. 2, pp. 379-399

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Using the standard theta series of genus $n$, the Hecke rings $\hat D=\hat D(\Gamma_0^n(q),S^n(q))$, for a covering $\mathfrak{G}$ of the symplectic group $GSp_n^+(\mathbf R)$ are constructed. The special role of four subrings of $\hat D$ is described, as well as some finitely generated arithmetic subrings $\hat L_p^n(\varkappa)$. The latter are important in the study of multiplicative properties of the Fourier coefficients of Siegel modular forms of half-integral weight. Bibliography: 11 titles. 
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     author = {V. G. Zhuravlev},
     title = {Hecke rings for a~covering of the symplectic group},
     journal = {Sbornik. Mathematics},
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V. G. Zhuravlev. Hecke rings for a~covering of the symplectic group. Sbornik. Mathematics, Tome 49 (1984) no. 2, pp. 379-399. http://geodesic.mathdoc.fr/item/SM_1984_49_2_a6/