Counting rational points on genus one curves
Licentiate thesis, 2017

This thesis contains two papers dealing with counting problems for curves of genus one. We obtain uniform upper bounds for the number of rational points of bounded height on such curves. The main tools to study these problems are descent and various refined versions of Heath-Brown’s p-adic determinant method. In the first paper, we count rational points on smooth plane cubic curves. In the second paper, we count rational points on non-singular complete intersections of two quadrics. The methods are different for curves of small height and large height and descent is only used for curves of small height.

genus

rational points

Diophantine equations

determinant method

descent

cubic and quartic curves

Elliptic curves

Pascal, Matematiska vetenskaper, Chalmers tvärgata 3
Opponent: Dr Oscar Marmon, University of Copenhagen, Denmark

Author

Manh Hung Tran

Chalmers, Mathematical Sciences, Algebra and geometry

Manh Hung Tran, Counting rational points on smooth cubic curves

Manh Hung Tran, Uniform bounds for rational points on complete intersections of two quadric surfaces

Subject Categories

Geometry

Publisher

Chalmers University of Technology

Pascal, Matematiska vetenskaper, Chalmers tvärgata 3

Opponent: Dr Oscar Marmon, University of Copenhagen, Denmark

More information

Created

3/28/2017