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
Keywords: Riesz capacity, Logarithmic capacity, Dobiński set, Dyadic capacity, Non-linear capacity, Diophantine approxmation
Nicola Arcozzi 1; Nikolaos Chalmoukis 1
@article{CRMATH_2022__360_G6_679_0, author = {Nicola Arcozzi and Nikolaos Chalmoukis}, 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}, year = {2022}, doi = {10.5802/crmath.332}, zbl = {07547266}, language = {en}, }
Nicola Arcozzi; Nikolaos Chalmoukis. Riesz capacities of a set due to Dobiński. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 679-685. doi : 10.5802/crmath.332. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.332/
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