English

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.

Keywords

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