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 $$ \sum{q\leq Q}\sum{a=1}^q\left\sum{\substack{n\leq x\n\equiv a\pmod q}}d(n)\frac{x}{q}\sum{t\mid q}\frac{ct(a)}{t}\left(\log\frac{x}{t^2}+2\gamma1\right)\right^2 $$ 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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Publication Date  January 1, 2018 
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Deposited  November 15, 2021 
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