In this paper, for a finite subset A subset of {2,3, center dot center dot center dot }, we introduce the notion of longest block function L-n (x,A) for the Luroth expansion of x epsilon [0,1) with respect to A and consider the asymptotic behavior of L-n (x,A) as n tends to infinity. We also obtain the Hausdorff dimensions of the level sets and exceptional set arising from the longest block function. (c) 2017 Elsevier Inc. All rights reserved.
Funding Agencies|National Natural Science Foundation of China [11671189, 11371148]; Natural Science Foundation of Fujian Province [2017J01403]; Program for New Century Excellent Talents in Fujian Province University