Geodesic
Rationality of generating series for the Fourier coefficient of Siegel modular forms of genus $n$
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions, Tome 76 (1978), pp. 65-71 
S. A. Evdokimov. Rationality of generating series for the Fourier coefficient of Siegel modular forms of genus $n$. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions, Tome 76 (1978), pp. 65-71. http://geodesic.mathdoc.fr/item/ZNSL_1978_76_a3/
@article{ZNSL_1978_76_a3,
     author = {S. A. Evdokimov},
     title = {Rationality of generating series for the {Fourier} coefficient of {Siegel} modular forms of genus~$n$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {65--71},
     year = {1978},
     volume = {76},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1978_76_a3/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

One proves the rationality of the multiple power series of the form $$ \sum_{\delta_1\geqslant0}\dots\sum_{\delta_r\geqslant0}a(p_1^{\delta_1}\dots p_r^{\delta_r}N) t_1^{\delta_1}\dots t_r^{\delta_r}, $$ where $a(\dots)$ is the Fourier coefficient of an arbitrary Siegel modular form of genus $n\ge 1$ relative to a congruence subgroup of the group $Sp_n(\mathbf Z)$, $p_1,\dots,p_r$ being a collection of prime numbers, dividing the step of the form.