Abstract
For any x∊(0,1], let the series ∑n = 1∞1/(d1(x)... dn(x)) be the Engel expansion of x. We show that for any 0<α<1, β∊R, there are points x such that log dn(x)−n∼βnα. Actually, the Hausdorff dimension of the set of such points is 1. We also prove that the points whose speed of convergence is faster than the `typical' points form a set of full Hausdorff dimension.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
