We study the Riesz -capacity of the so called Dobiński set. We characterize the values of the parameters and for which the -Riesz capacity of the Dobiński set is positive. In particular we show that the Dobiński set has positive logarithmic capacity, thus answering a question of Dayan, Fernandéz and González. We approach the problem by considering the dyadic analogues of the Riesz -capacities which seem to be better adapted to the problem.
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DOI : 10.5802/crmath.332
Mots clés : Riesz capacity, Logarithmic capacity, Dobiński set, Dyadic capacity, Non-linear capacity, Diophantine approxmation
@article{CRMATH_2022__360_G6_679_0,
author = {Arcozzi, Nicola and Chalmoukis, Nikolaos},
title = {Riesz capacities of a set due to {Dobi\'nski}},
journal = {Comptes Rendus. Math\'ematique},
pages = {679--685},
publisher = {Acad\'emie des sciences, Paris},
volume = {360},
number = {G6},
year = {2022},
doi = {10.5802/crmath.332},
zbl = {07547266},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/crmath.332/}
}
TY - JOUR AU - Arcozzi, Nicola AU - Chalmoukis, Nikolaos TI - Riesz capacities of a set due to Dobiński JO - Comptes Rendus. Mathématique PY - 2022 SP - 679 EP - 685 VL - 360 IS - G6 PB - Académie des sciences, Paris UR - http://archive.numdam.org/articles/10.5802/crmath.332/ DO - 10.5802/crmath.332 LA - en ID - CRMATH_2022__360_G6_679_0 ER -
%0 Journal Article %A Arcozzi, Nicola %A Chalmoukis, Nikolaos %T Riesz capacities of a set due to Dobiński %J Comptes Rendus. Mathématique %D 2022 %P 679-685 %V 360 %N G6 %I Académie des sciences, Paris %U http://archive.numdam.org/articles/10.5802/crmath.332/ %R 10.5802/crmath.332 %G en %F CRMATH_2022__360_G6_679_0
Arcozzi, Nicola; Chalmoukis, Nikolaos. Riesz capacities of a set due to Dobiński. Comptes Rendus. Mathématique, Tome 360 (2022) no. G6, pp. 679-685. doi : 10.5802/crmath.332. http://archive.numdam.org/articles/10.5802/crmath.332/
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