Integral points on elliptic curves and -torsion in class groups |
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Authors: | H A Helfgott A Venkatesh |
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Institution: | Department of Mathematics, Yale University, New Haven, Connecticut 06520 ; Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139--4307 |
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Abstract: | We give new bounds for the number of integral points on elliptic curves. The method may be said to interpolate between approaches via diophantine techniques and methods based on quasi-orthogonality in the Mordell-Weil lattice. We apply our results to break previous bounds on the number of elliptic curves of given conductor and the size of the -torsion part of the class group of a quadratic field. The same ideas can be used to count rational points on curves of higher genus. |
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Keywords: | Class groups elliptic curves integral points |
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