Abstract
Using hypergeometric functions and the Thue–Siegel method we give an effective improvement of Liouville's approximation theorem. As an application, we derive effective upper bounds for the solutions ( X, Y) of the two-parametric family of quartic Thue inequalities |BX 4−AX 3Y−6BX 2Y 2+AXY 3+BY 4|⩽N for A⩾58| B| 3 or A⩾308 B 4.
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