Numbers with Almost all Convergents in a Cantor Set
Canadian mathematical bulletin, Tome 62 (2019) no. 4, pp. 869-875
Voir la notice de l'article provenant de la source Cambridge
In 1984, K. Mahler asked how well elements in the Cantor middle third set can be approximated by rational numbers from that set and by rational numbers outside of that set. We consider more general missing digit sets $C$ and construct numbers in $C$ that are arbitrarily well approximable by rationals in $C$, but badly approximable by rationals outside of $C$. More precisely, we construct them so that all but finitely many of their convergents lie in $C$.
Mots-clés :
Cantor set, continued fraction, Diophantine approximation, parametric geometry of numbers
Roy, Damien; Schleischitz, Johannes. Numbers with Almost all Convergents in a Cantor Set. Canadian mathematical bulletin, Tome 62 (2019) no. 4, pp. 869-875. doi: 10.4153/S0008439518000450
@article{10_4153_S0008439518000450,
author = {Roy, Damien and Schleischitz, Johannes},
title = {Numbers with {Almost} all {Convergents} in a {Cantor} {Set}},
journal = {Canadian mathematical bulletin},
pages = {869--875},
year = {2019},
volume = {62},
number = {4},
doi = {10.4153/S0008439518000450},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439518000450/}
}
TY - JOUR AU - Roy, Damien AU - Schleischitz, Johannes TI - Numbers with Almost all Convergents in a Cantor Set JO - Canadian mathematical bulletin PY - 2019 SP - 869 EP - 875 VL - 62 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/S0008439518000450/ DO - 10.4153/S0008439518000450 ID - 10_4153_S0008439518000450 ER -
%0 Journal Article %A Roy, Damien %A Schleischitz, Johannes %T Numbers with Almost all Convergents in a Cantor Set %J Canadian mathematical bulletin %D 2019 %P 869-875 %V 62 %N 4 %U http://geodesic.mathdoc.fr/articles/10.4153/S0008439518000450/ %R 10.4153/S0008439518000450 %F 10_4153_S0008439518000450
Cité par Sources :