Promotor: Prof.dr. P. Stevenhagen, Co-Promotor: J.H. Evertse
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With focus on study of binary forms and their discriminants and resultants over function fields, we developed an analogue of the geometry of numbers and generalized Mason's ABC theorem. Then we proved a conjecture, which is possibly first formulated by Evertse, over the rational function field and effectively bounded S-distance of algebraic functions, and improved results of root separation problem.