The divisor function in arithmetic progressions modulo prime powers

Abstract

We study the average value of the divisor function $\tau (n)$ for $n\le x$ with $n\equiv a\mathrm{mod}q$. The divisor function is known to be evenly distributed over arithmetic progressions for all $q$ that are a little smaller than $x^{2/3}$. We show how to go past this barrier when $q=p^k$ for odd primes $p$ and any fixed integer $k\ge 7$.

8 pages

References in corpus (2)

• The second moment of twisted modular L-functions
• Sub-Weyl subconvexity for Dirichlet L-functions to prime power moduli

Cited by in corpus (1)

• On a conjecture of Soundararajan