Jacobsthal's function and a generalisation of Euler's totient
Number Theory
2012-09-20 v2
Abstract
Jacobsthal's function h(k) represents the smallest number m such that every sequence of m consecutive integers contains an integer coprime to P_k, the product of the first k primes. The best known bound on h(k) is h(k) < C (k ln k)^2 for some unknown constant C, due to Iwaniec. We use a generalisation of Euler's totient function to give a stronger bound on h(k).
Cite
@article{arxiv.1209.3464,
title = {Jacobsthal's function and a generalisation of Euler's totient},
author = {Fintan Costello and Paul Watts},
journal= {arXiv preprint arXiv:1209.3464},
year = {2012}
}
Comments
This paper has been withdrawn due to an error on page 6