Linear Forms in Logarithms and Integer Points on Genus-two Curves

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.

Department dc:contributor.department

Mathematics

Year dc:date.issued

2006

Author dc:creator

• Vogler, John Richard

Advisor dc:contributor.advisor

• Washington, Lawrence C

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/1903/4180

OAI identifier oai:identifier

oai:drum.lib.umd.edu:1903/4180