On the square-free sieve

H. A. Helfgott

Type: Article

Publication Date: 2004-01-01

Citations: 21

DOI: https://doi.org/10.4064/aa115-4-3

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.

Locations

Acta Arithmetica - View - PDF
arXiv (Cornell University) - View - PDF
DataCite API - View

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+	Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2	1996	J. W. S. Cassels E. V. Flynn
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