On the Hyper-geometric Function Value Approximation to the Parameter from the Real Quadratic Field
While studying arithmetic properties of the values of the generalized hyper-geometric functions there is always a need, arising in the process of reasoning, to have the lower estimate of the modulus of a nonzero algebraic integer. This estimate meets all the requirements only if the above-mentioned algebraic integer is rational or belongs to some imaginary quadratic field. It is by no means always possible to overcome difficulties caused by fact that a nonzero algebraic integer from the arbitrary algebraic field may be arbitrarily small.