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arXiv · 1609.08183

The asymptotic behavior of limit-periodic functions on primes and an application to k-free numbers

Markus Hablizel
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Abstract

We use the circle method to evaluate the behavior of limit-periodic functions on primes. For those limit-periodic functions that satisfy a kind of Barban-Davenport-Halberstam condition and whose singular series converge fast enough, we can evaluate their average value on primes. As an application, this result is used to show how tuples of different k-free numbers behave when linear shifts are applied.

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Markus Hablizel. 2016-09-26. The asymptotic behavior of limit-periodic functions on primes and an application to k-free numbers. https://arxiv.org/abs/1609.08183

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