Timeline for Analytic continuation of an Integral involving product of L-functions

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Oct 13, 2016 at 0:22	history	edited	GH from MO		edited tags
Oct 13, 2016 at 0:02	comment	added	Ted Mao		@user1952009 Thanks for the comment. I am actually looking at the case when the L-functions are Hecke L-functions. Edited the question.
Oct 12, 2016 at 23:59	history	edited	Ted Mao	CC BY-SA 3.0	added 292 characters in body
Oct 12, 2016 at 23:40	comment	added	reuns		using that $\langle f ,g \rangle = \langle \hat{f},\hat{g} \rangle$ I get something like $\sum_{n=1}^\infty \chi_2(n)n^{-s} (\sum_{k < n} \chi_1(k)) $. Since $a(n) = \chi_2(n)\sum_{k < n} \chi_1(k)$ is periodic, $\sum_{n=1}^\infty a(n) n^{-s}$ is entire except a simple pole at $s=1$ of residue the mean value of $a(n)$
Oct 12, 2016 at 22:39	history	asked	Ted Mao	CC BY-SA 3.0