Explicit bounds for large gaps between squarefree integers

2022/11/18 by Angel Kumchev, Kumchev, Angel, Wade McCormick +8
Mathematics · #Limits and Structures in Graph Theory #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.2211.09975

Abstract

We obtain explicit forms of the current best known asymptotic upper bounds for gaps between squarefree integers. In particular we show, for any x ≥ 2, that every interval of the form (x, x + 11x^1/5log x] contains a squarefree integer. The constant 11 can be improved further, if x is assumed to be larger than a (very) large constant.

Related

• New small gaps between squarefree numbers
• Squarefree numbers in short intervals
• Large gaps between sums of two squareful numbers
• An explicit lower bound for large gaps between some consecutive primes
• On the distribution of squarefree integers in arithmetic progressions