Fractal projections with an application in number theory

2020/04/13 by Yu Han, Yu, Han
Mathematics · #Mathematical Dynamics and Fractals #Mathematical and Theoretical Analysis #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.2004.05924

Abstract

In this paper, we discuss a connection between geometric measure theory and number theory. This method brings a new point of view for some number-theoretic problems concerning digit expansions. Among other results, we showed that for each integer k, there is a number M>0 such that if b₁,…,b_k are multiplicatively independent integers greater than M, there are infinitely many integers whose base b₁,b₂,…,b_k expansions all do not have any zero digits.

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