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THE DIVISOR FUNCTION IN ARITHMETIC PROGRESSIONS MODULO PRIME POWERS
Published online by Cambridge University Press: 17 May 2016
Abstract
We study the average value of the divisor function $\unicode[STIX]{x1D70F}(n)$ for
$n\leqslant x$ with
$n\equiv a~\text{mod}~q$. 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
$k\geqslant 7$.
MSC classification
- Type
- Research Article
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- Copyright
- Copyright © University College London 2016
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