Geodesic
Continuation of Siegel modular forms to the Siegel--Satake half-plane
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 8, Tome 160 (1987), pp. 99-109

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With the aid of the continuation of the Siegel modular forms to the Siegel–Satake half-plane one establishes the relation between the Siegel operators and Hecke operators for modular forms with respect to subgroups of finite index of the group $Sp_n(Z)$. 
@article{ZNSL_1987_160_a9,
     author = {N. A. Zharkovskaya},
     title = {Continuation of {Siegel} modular forms to the {Siegel--Satake} half-plane},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {99--109},
     publisher = {mathdoc},
     volume = {160},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_160_a9/}
}
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N. A. Zharkovskaya. Continuation of Siegel modular forms to the Siegel--Satake half-plane. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 8, Tome 160 (1987), pp. 99-109. http://geodesic.mathdoc.fr/item/ZNSL_1987_160_a9/