Diophantine equations over function fields

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We shall often take a more geometric point of view. These questions include problems on lacunary rational functions that are composite, rational and integral points on fibered surfaces also in connection with problems related to linear recurrences and families of classical Diophantine equations over function fields, and Diophantine tuples. The project has ended on Open Positions: Currently there are no positions open in this project. Karolus: Invitation PhD thesis of C.

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Karolus added on September 12, ! Number Theory! Then the number of distinct roots of the three polynomials is one or more greater than their largest degree. The theorem was first proved by Stothers Mason's theorem may be viewed as a very special case of a Wronskian estimate Chudnovsky and Chudnovsky The corresponding Wronskian identity in the proof by Lang is.

More powerful Wronskian estimates with applications toward Diophantine approximation of solutions of linear differential equations may be found in Chudnovsky and Chudnovsky and Osgood The rational function case of Fermat's last theorem follows trivially from Mason's theorem Lang , p. Chudnovsky, D. Dubuque, W. Lang, S.

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Algebra, 3rd ed. Reading, MA: Addison-Wesley, Mason, R. Diophantine Equations over Functions Fields. Cambridge, England: Cambridge University Press, Osgood, C. Number Th.

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