
The divisor function on residue classes II
Let $d(n)$ and $ct(a)$ denote the number of positive divisors of $n$ and the Ramanujan sum, respectively. The asymptotic formula for $$ \sum{q\leq Q}\sum{a=1}^q\left|\sum{\substack{n\leq x\n\equiv a\pmod q}}d(n)-\frac{x}{q}\sum{t\mid q}\frac{ct(a)}{t}\left(\log\frac{x}{t^2}+2\gamma-1\right)\right|^2 $$ is established for a wide range of $Q$. This generalises Motohashi's result \cite{Mot} which deals only with the special case $Q = x$ and has only a larger error term.
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Work Title | The divisor function on residue classes II |
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License | In Copyright (Rights Reserved) |
Work Type | Article |
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Publication Date | January 1, 2018 |
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Deposited | November 15, 2021 |
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