On the square-free sieve

Details On the square-free sieve On the square-free sieve

2003-09-05

arxiv.org/abs/math/0309109v4

Mathematics

Number Theory

51 pages; typos fixed

Scientific paper

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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