$p$-adic quotient sets
Acta Arithmetica, Tome 179 (2017) no. 2, pp. 163-184
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
For $A \subseteq \mathbb{N}$, the question of when $R(A) = \{a/a’ : a, a’ \in A\}$ is dense in the positive real numbers $\mathbb{R}_+$ has been examined by many authors over the years. In contrast, the $p$-adic setting is largely unexplored. We investigate conditions under which $R(A)$ is dense in the $p$-adic numbers. Techniques from elementary, algebraic, and analytic number theory are employed. We also pose many open questions that should be of general interest.
Mots-clés :
subseteq mathbb question dense positive real numbers mathbb has examined many authors years contrast p adic setting largely unexplored investigate conditions under which dense p adic numbers techniques elementary algebraic analytic number theory employed pose many questions should general interest
Affiliations des auteurs :
Stephan Ramon Garcia 1 ; Yu Xuan Hong 2 ; Florian Luca 3 ; Elena Pinsker 2 ; Carlo Sanna 4 ; Evan Schechter 2 ; Adam Starr 2
@article{10_4064_aa8579_4_2017,
author = {Stephan Ramon Garcia and Yu Xuan Hong and Florian Luca and Elena Pinsker and Carlo Sanna and Evan Schechter and Adam Starr},
title = {$p$-adic quotient sets},
journal = {Acta Arithmetica},
pages = {163--184},
year = {2017},
volume = {179},
number = {2},
doi = {10.4064/aa8579-4-2017},
language = {fr},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa8579-4-2017/}
}
TY - JOUR AU - Stephan Ramon Garcia AU - Yu Xuan Hong AU - Florian Luca AU - Elena Pinsker AU - Carlo Sanna AU - Evan Schechter AU - Adam Starr TI - $p$-adic quotient sets JO - Acta Arithmetica PY - 2017 SP - 163 EP - 184 VL - 179 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4064/aa8579-4-2017/ DO - 10.4064/aa8579-4-2017 LA - fr ID - 10_4064_aa8579_4_2017 ER -
%0 Journal Article %A Stephan Ramon Garcia %A Yu Xuan Hong %A Florian Luca %A Elena Pinsker %A Carlo Sanna %A Evan Schechter %A Adam Starr %T $p$-adic quotient sets %J Acta Arithmetica %D 2017 %P 163-184 %V 179 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4064/aa8579-4-2017/ %R 10.4064/aa8579-4-2017 %G fr %F 10_4064_aa8579_4_2017
Stephan Ramon Garcia; Yu Xuan Hong; Florian Luca; Elena Pinsker; Carlo Sanna; Evan Schechter; Adam Starr. $p$-adic quotient sets. Acta Arithmetica, Tome 179 (2017) no. 2, pp. 163-184. doi: 10.4064/aa8579-4-2017
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