Geodesic
On reduction modulo a prime of fields of modular functions
Izvestiya. Mathematics , Tome 2 (1968) no. 6, pp. 1213-1222.

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We study the reduction modulo $p$ of a subring of the field of modular functions $K(p^\infty)$ modulo $p$. We obtain a generalization of a known congruence of Weber. 
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I. I. Pyatetskii-Shapiro. On reduction modulo a prime of fields of modular functions. Izvestiya. Mathematics , Tome 2 (1968) no. 6, pp. 1213-1222. http://geodesic.mathdoc.fr/item/IM2_1968_2_6_a2/

[1] Pyatetskii-Shapiro I. I., Shafarevich I. R., “Teoriya Galua transtsendentnykh rasshirenii i uniformizatsiya”, Izv. AN SSSR. Ser. matem., 30 (1966), 671–704

[2] Shimura G., “Correspondances modulaires et les fonctions $\zeta$ de courbes algebriques”, J. Math. Soc. Japan., 10 (1958), 1–28 | MR | Zbl

[3] Weber H., Algebra, b. 3, Braunschweig, 1908

[4] Gelfand I. M., Naimark M. A., “Unitarnye predstavleniya gruppy Lorentsa”, Izv. AN SSSR. Ser. matem., 11 (1947), 411–504 | MR