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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 $k\geqslant 7$.
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- Research Article
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- Copyright © University College London 2016
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