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Counting Rational Points on Cubic Curves

Research paper by D. R. Heath-Brown, D. Testa

Indexed on: 23 Sep '09Published on: 23 Sep '09Published in: Mathematics - Number Theory



Abstract

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.