Moments of the distribution of \(k\)-free numbers in short intervals and arithmetic progressions

Moments of the distribution of \(k\)-free numbers in short intervals and arithmetic progressions

We show estimates for the distribution of \(k\)-free numbers in short intervals and arithmetic progressions. We argue that, at least in certain ranges, these estimates agree with a conjecture by H. L. Montgomery.

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Veröffentlicht in:arXiv.org 2020-10
1. Verfasser: Nunes, Ramon M
Format: Artikel
Sprache:eng
Schlagworte:
Arithmetic
Intervals
Numbers
Progressions
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Zusammenfassung:We show estimates for the distribution of \(k\)-free numbers in short intervals and arithmetic progressions. We argue that, at least in certain ranges, these estimates agree with a conjecture by H. L. Montgomery.
ISSN:2331-8422