Counting rationals and diophantine approximation in missing-digit Cantor sets
Year: 2026
Type: article
Abstract: We establish a new upper bound for the number of rationals up to a given height in a missing-digit set, making progress towards a conjecture of Broderick, Fishman, and Reich. This enables us to make novel progress towards another conjecture of those authors about the corresponding intrinsic diophantine approximation problem. Moreover, we make further progress towards conjectures of Bugeaud–Durand and Levesley–Salp–Velani on the distribution of diophantine exponents in missing-digit sets. A key tool in our study is Fourier ℓ 1 dimension introduced by the last named author in Yu (2021) [12] . An important technical contribution of the paper is a method to compute this quantity.
Source: Advances in Mathematics
Authors: Sam Chow, Péter P. Varjú, Han Yu
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,790
Funders: Leverhulme Trust, Royal Society, University of Cambridge, European Commission, Vetenskapsrådet, Horizon 2020 Framework Programme, Engineering and Physical Sciences Research Council, Christ's College, University of Cambridge, Corpus Christi College, University of Cambridge, European Research Council
OpenAlex ID: W7125419937