On the divisor problem in arithmetic progressions

Abstract: 

Selberg and Hooley considered the divisor problem in the arithmetic progression a+qna+qn, n=1,2,3,…n=1,2,3,….  Using the Weil bound for Kloosterman sums, they obtained (independently) a classical upper bound for the error term in the related asymptotic formula. In this talk, I will discuss the case that q is a prime power, where we can do better than Selberg and Hooley. This is joint work with Igor Shparlinski and Tianping Zhang.