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arXiv · 1510.03377

The divisor function in arithmetic progressions modulo prime powers

Rizwanur Khan
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Abstract

We study the average value of the divisor function $τ(n)$ for $n\le x$ with $n \equiv a \bmod q$. 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 $k\ge 7$.

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Rizwanur Khan. 2016-02-12. The divisor function in arithmetic progressions modulo prime powers. https://doi.org/10.1112/s0025579316000024

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