Titchmarsh divisor problem for almost primes

In 1976, Fujii obtained an asymptotic formula for an analogue of the Titchmarsh divisor problem for the product of two primes. Recently, Drappeau and Topacogullari studied an asymptotic formula for the Titchmarsh divisor problem with a small shift for almost primes. In this talk, we will discuss an asymptotic formula for the Titchmarsh divisor problem for the product of primes, which is uniform in the shift parameter.