Cristian Cobeli, Alexandru Zaharescu
Published 2005-11-14Version 1
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.
On the distribution of the order and index of g(mod p) over residue classes
On the distribution of the order and index of g(mod p) over residue classes III
The distribution of the variance of primes in arithmetic progressions
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