Counting rational points on genus one curves

Detta är en avhandling från Chalmers University of Technology

Författare: Manh Hung Tran; Chalmers Tekniska Högskola Göteborgs Universitet.; Chalmers University Of Technology University Of Gothenburg.; [2017]

Nyckelord: NATURVETENSKAP; NATURAL SCIENCES; Diophantine equations; rational points; Elliptic curves; genus; descent; determinant method; cubic and quartic curves;

Sammanfattning: 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.

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