1Department of Mathematics Pomona College 610 N. College Ave. Claremont, CA 91711, U.S.A. <a href="http://pages.pomona.edu/~sg064747">http://pages.pomona.edu/~sg064747</a> 2Department of Mathematics Pomona College 610 N. College Ave. Claremont, CA 91711 3School of Mathematics University of the Witwatersrand Private Bag 3 Wits 2050, Johannesburg, South Africa and Max Planck Institute for Mathematics Vivatsgasse 7 53111 Bonn, Germany 4Department of Mathematics Università degli Studi di Torino Via Carlo Alberto, 10 10123 Torino, Italy
Acta Arithmetica, Tome 179 (2017) no. 2, pp. 163-184
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
1
Department of Mathematics Pomona College 610 N. College Ave. Claremont, CA 91711, U.S.A. <a href="http://pages.pomona.edu/~sg064747">http://pages.pomona.edu/~sg064747</a>
2
Department of Mathematics Pomona College 610 N. College Ave. Claremont, CA 91711
3
School of Mathematics University of the Witwatersrand Private Bag 3 Wits 2050, Johannesburg, South Africa and Max Planck Institute for Mathematics Vivatsgasse 7 53111 Bonn, Germany
4
Department of Mathematics Università degli Studi di Torino Via Carlo Alberto, 10 10123 Torino, Italy
@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
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DO - 10.4064/aa8579-4-2017
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%J Acta Arithmetica
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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
