2023/03/06 by David Harry Richman, Richman, David Harry
Computer Science · Mathematics · #11B57 (Primary) 40A30 #11B83 (Secondary) #11J70 #26D15 #40A25 #Computability, Logic, AI Algorithms #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Numerical Methods and Algorithms
paper · pdf · doi:10.48550/arxiv.2303.02935
openalex publication_date 2023/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a real number x, call \frac1n \lfloor nx \rfloor the n-th lower rational approximation of x. We study the functions defined by taking the cumulative average of the first n lower rational approximations of x, which we call the Farey staircase functions. This sequence of functions is monotonically increasing. We determine limit behavior of these functions and show that they exhibit fractal structure under appropriate normalization.