Applications of the Large Sieve Inequality for q[T]

The purpose of this note is the following: (1) To get an upper bound for the number of monic irreducible polynomials in q[T] obtained by changing coefficients of a polynomial in lower degree terms. (2) To generalize the Titchmarsh Linnik divisor problem to polynomial ring q[T] and prove an asymptotic formula for this divisor function.