2005/11/14 by Cristian Cobeli, Alexandru Zaharescu, Cobeli, Cristian +1
Mathematics · #11B57 (primary) #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications #Number Theory (math.NT) #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.math/0511356
openalex publication_date 2005/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Our purpose is to give an account of the r-tuple problem on the increasing sequence of reduced fractions having denominators bounded by a certain size and belonging to a fixed real interval. We show that when the size grows to infinity, the proportion of the r-tuples of consecutive denominators with components in certain apriori fixed arithmetic progressions with the same ratio approaches a limit, which is independent on the interval. The limit is given explicitly and it is completely described in a few particular instances.