Geodesic
Sets of recurrence as bases for the positive integers
Jakub Konieczny1
1 Mathematical Institute University of Oxford Andrew Wiles Building Radcliffe Observatory Quarter Woodstock Road Oxford, OX2 6GG, U.K.
Acta Arithmetica, Tome 174 (2016) no. 4, pp. 309-338.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We study sets of the form $\mathcal{A} = \{ n \in \mathbb {N} \mid \|{p(n)}\| \leq \varepsilon(n) \}$ for various real valued polynomials $p$ and decay rates $\varepsilon$. In particular, we ask when such sets are bases of finite order for the positive integers. We show that generically, $\mathcal A$ is a basis of order 2 when $\deg p \geq 3$, but not when $\deg p = 2$, although then $\mathcal A + \mathcal A$ still has asymptotic density $1$.
DOI : 10.4064/aa8125-4-2016
Keywords: study sets form mathcal mathbb mid leq varepsilon various real valued polynomials decay rates varepsilon particular ask sets bases finite order positive integers generically mathcal basis order nbsp deg geq deg although mathcal mathcal still has asymptotic density nbsp

Jakub Konieczny 1

1 Mathematical Institute University of Oxford Andrew Wiles Building Radcliffe Observatory Quarter Woodstock Road Oxford, OX2 6GG, U.K. 
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Jakub Konieczny. Sets of recurrence as bases for the positive integers. Acta Arithmetica, Tome 174 (2016) no. 4, pp. 309-338. doi : 10.4064/aa8125-4-2016. http://geodesic.mathdoc.fr/articles/10.4064/aa8125-4-2016/

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