Geodesic
On the measure of algebraic independence of values of derivatives of a~$p$-adic modular function
Matematičeskie zametki, Tome 61 (1997) no. 3, pp. 431-440.

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The measure of the relative transcendence for the values of the derivatives of a $p$-adic Weyl–Lutz modular function $J(q)$ at algebraic points is estimated. 
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A. Ya. Yanchenko. On the measure of algebraic independence of values of derivatives of a~$p$-adic modular function. Matematičeskie zametki, Tome 61 (1997) no. 3, pp. 431-440. http://geodesic.mathdoc.fr/item/MZM_1997_61_3_a11/

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