We give asymptotics for a shifted convolution of sum-of-divisors functions twisted by Dirichlet characters and with nonzero powers. We'll use the technique of "automorphic regularization'' to find the spectral decomposition of a combination of Eisenstein series which is not obviously square-integrable.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/3444
[3] http://www.mpim-bonn.mpg.de/de/node/11531