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Washington, Lawrence C Vogler, John Richard Digital Repository at the University of Maryland University of Maryland (College Park, Md.) Mathematics 2007-02-01T20:22:58Z 2007-02-01T20:22:58Z 2006-11-27 http://hdl.handle.net/1903/4180 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. 546246 bytes application/pdf en_US Linear Forms in Logarithms and Integer Points on Genus-two Curves Dissertation Mathematics number theory transcendental number theory diophantine approximation diophantine equation jacobian logarithmic form open.access