Volker Ziegler: Relative Thue equations, Baker's method vs. hypergeometric method

Let $ F(X,Y) \in R[X,Y]$ be a homogenous polynomial, where $ R$ is some order of some number field, then the diophantine equation $ F(X,Y)=\mu$ with $ \mu \in R$ is called a relative Thue equation, if $ R$ are not the integers. In this talk we consider two families of relative Thue equations over imaginary quadratic number fields. One family is solved by using estimates on linearforms in logarithms (Baker's Method) and the other family is solved by constructing Pade approximations, that yield an effective measure of irrationality of some algebraic numbers (Method of Thue-Siegel). Advantages and disadvantages of both methods are demonstrated.

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