English

Hausdorff Measures, Dyadic Approximations and Dobi\'nski Set

Number Theory 2019-11-15 v1 Classical Analysis and ODEs

Abstract

Dobi\'nski set D\mathcal{D} is an exceptional set for a certain infinite product identity, whose points are characterized as having exceedingly good approximations by dyadic rationals. We study the Hausdorff dimension and logarithmic measure of D\mathcal{D} by means of the Mass Transference Principle and by the construction of certain appropriate Cantor-like sets, termed willow sets, contained in D\mathcal{D}.

Keywords

Cite

@article{arxiv.1911.05915,
  title  = {Hausdorff Measures, Dyadic Approximations and Dobi\'nski Set},
  author = {Alberto Dayan and José L. Fernández and María J. González},
  journal= {arXiv preprint arXiv:1911.05915},
  year   = {2019}
}
R2 v1 2026-06-23T12:15:21.906Z