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On the square-free sieve

Harald Helfgott
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Abstract

We improve on the best available bounds for the square-free sieve and provide a general framework for its applicability. The failure of the local-to-global principle allows us to obtain results better than those reached by a classical sieve-based approach. Techniques involving sphere-packing yield upper bounds on the number of integer and rational points on curves of positive genus.

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Harald Helfgott. 2004-10-01. On the square-free sieve. https://doi.org/10.4064/aa115-4-3

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