On the square-free sieve
Number Theory
2015-06-26 v4 Algebraic Geometry
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.
Cite
@article{arxiv.math/0309109,
title = {On the square-free sieve},
author = {Harald Helfgott},
journal= {arXiv preprint arXiv:math/0309109},
year = {2015}
}
Comments
51 pages; typos fixed