Counting Rational Points on Cubic Curves

Details Counting Rational Points on Cubic Curves Counting Rational Points on Cubic Curves

2009-09-23

arxiv.org/abs/0909.4246v1

Mathematics

Number Theory

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Scientific paper

We prove upper bounds for the number of rational points on non-singular cubic
curves defined over the rationals. The bounds are uniform in the curve and
involve the rank of the corresponding Jacobian. The method used in the proof is
a combination of the "determinant method" with an m-descent on the curve.

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