# On the divisor problem in arithmetic progressions

Kui Liu

## Affiliation:

Qingdao University

## Date:

Wed, 10/08/2016 - 2:00pm

## Venue:

RC-4082, The Red Centre, UNSW

## Abstract:

Selberg and Hooley considered the divisor problem in the arithmetic progression $a+qn$, $n=1,2,3,\ldots$.  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.