Divisor problem in arithmetic progressions modulo a prime power

Speaker: 刘奎 (青岛大学)

Venue: B1044

Time: 2018年01月05日   15:00-16:00

Title: Divisor problem in arithmetic progressions modulo a prime power

Abstract: We obtain an asymptotic formula for the average value of the divisorfunction over the integers $n le x$ in an arithmetic progression $n equiv a bmod q$,where $q=p^k$ for a prime $pge 3$ and a sufficiently large integer $k$. In particular, we breakthe classical barrier $q le x^{2/3-varepsilon}$ (with an arbitrary $varepsilon>0$) for such formulas, and, using some new arguments, generalise and strengthen a recent result of R. Khan (2015), making it uniform in $k$.