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Linear forms in logarithms and integer points on genus -two curves

Title of dissertation: LINEAR FORMS IN LOGARITHMS AND INTEGER POINTS ON GENUS-TWO CURVES John Vogler, Doctor of Philosophy, 2006 Dissertation directed by: Professor Lawrence C. Washington Department of Mathematics We consider a linear form with algebraic coefficients, evaluated at points on the analytic Jacobian of a genus-two curve whose projective coordinates are algebraic. Previous results on the existence of a lower bound of a particular shape are made explicit. We study various properties of Jacobians of genus-two curves, paying particular attention to their embeddings into projective space, and give a method which can be used to find provably all integer points on a genus-two curve. We apply this method to one particular curve by way of example. LINEAR FORMS IN LOGARITHMS AND INTEGER POINTS ON GENUS-TWO CURVES