Jacobsthal's function and a generalisation of Euler's totient

2012/09/16 by Fintan Costello, Costello, Fintan, Paul Watts +1
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1209.3464

This paper has been withdrawn due to an error on page 6

arxiv created 2012/09/19 · arxiv updated 2012/09/20

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).

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