Valeriya Kovaleva

On integers divisible by a shifted prime in a given interval

Let H(x,y,z) be the number of integers with a divisor in a given interval (y,z]. Counting such integers is closely related to the multiplication table problem. In 2008, Ford found the order of magnitude of H(x,y,z) in all ranges of interest. In this talk we consider a variant of this problem, where the divisors are restricted to shifted primes. We observe multiple phase transitions in the behaviour of the adjusted function as well as the anatomy of integers possessing shifted prime divisors in a prescribed interval depending on its logarithmic length. This is joint work with R. Abi Abdallah, J. Schlitt, and N. Tardy.