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Preprint . 2016
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zbMATH Open
Article . 2017
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On the distribution of $\alpha p^{\gamma}+\beta$ modulo one

On the distribution of \(\alpha p^{\gamma}+\beta\) modulo one
descriptionPublicationkeyboard_double_arrow_right Preprint , Article 11 Sep 2016Publisher:Elsevier (Academic Press), San Diego, CA
Authors: Dunn, Alexander;

arXiv: 1609.03188

On the distribution of $\alpha p^{\gamma}+\beta$ modulo one

Abstract

Let $\|\cdot\|$ denote the minimum distance to an integer. For $00$ and $(\alpha, \beta) \in \mathbb{R} \setminus \{0\} \times \mathbb{R}$ we study when \begin{equation*} \|\alpha p^{\gamma}+\beta \|

Comment: Error in the proof of the main Lemma where the large sieve is applied

Keywords

Mathematics - Number Theory, linear sieve, Diophantine approximation, Applications of sieve methods, Distribution modulo one, exponential sums

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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