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Residue of the following variant of Dirichlet function [closed]

I am working with the Piltz divisor problem where the number of ways in which a number $n$ can be written as a product of $k$ is of the form $$D_{k}(x)=xP_{k}(\log x)+\Delta _{k}(x)$$ where $P_k$ is …
Shivin Srivastava's user avatar