TITLE: Origin of the notation s=\sigma+it in analytic number theory
QUESTION [7 upvotes]: I was wondering if the standard notation of denoting a complex variable by "$s$" had an interesting origin, or if it dates back to Riemann or Weierstrass. Almost every book in analytic number theory seems to uses that alphabet with 
$ s = \sigma + i t$ 
denoting its real and imaginary parts. 
I shall be happy if anyone could enlighten me about it. I tried searching MO for relevant questions but couldn't find it.

REPLY [5 votes]: In skimming through Narkiewicz "The Development of Prime Number Theory", one sees a reference on p. 155 (footnote 38) to a R. Lipschitz, who in Crelle volume 54 in 1857 "studied the series $\sum_{n=1}^\infty\exp(nui)n^{-\sigma}$ for real values of $\sigma$."  I checked the reference, which is here (there are two papers by Lipschitz in this volume of Crelle, and it's the second one that's relevant); Lipschitz was indeed using $\sigma$.  
Lipschitz is referred to several times in this section of Narkiewicz for later work on functional equations of various $L$-functions.