Geodesic
Induced rings and the reduction of fields of Abelian modular functions
Izvestiya. Mathematics , Tome 4 (1970) no. 3, pp. 536-550.

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The main result of the present paper is that a ring obtained by reduction of Abelian modular functions is a ring of functions on a $p$-adic symplectic group over a perfect field $k$ of characteristic $p$, and the ring is induced by a homomorphism of a parabolic subgroup on $\operatorname{Aut}k$. 
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     title = {Induced rings and the reduction of fields of {Abelian} modular functions},
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I. I. Pyatetskii-Shapiro. Induced rings and the reduction of fields of Abelian modular functions. Izvestiya. Mathematics , Tome 4 (1970) no. 3, pp. 536-550. http://geodesic.mathdoc.fr/item/IM2_1970_4_3_a4/

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