Euler expansions of theta transforms of Siegel modular forms of half-integral weight and their analytic properties

Using the method of A. N. Andrianov, we establish a connection between the Fourier coefficients of Siegel modular forms $F$ of half-integral weight and the eigenvalues of operators in the local Hecke rings $\mathbf L_p^n(\varkappa)$ for the symplectic covering group $\mathrm{GSp}_n^+(\mathbf R)$ of degree $n$. These results are used for analytic continuation of the standard zeta-functions associated to $F$.
Bibliography: 10 titles.