Arithmetic properties of the values of a class of analytic functions

In this paper conditions are established under which the values of the given set of $G$-functions at points of an imaginary quadratic field $I$ sufficiently small in modulus are not connected by a linear equation or an equation of degree $N$ with integral coefficients in $I$ no larger than $H$ in modulus. The modulus of the corresponding linear form and the modulus of a polynomial in the values of the $G$-functions are also estimated.
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