Timeline for On the Dirichlet series for $1/\zeta(s)$ for real $s$ and the zeros of zeta

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Dec 8, 2019 at 6:04	history	edited	Ali Taghavi		edited tags
Sep 19, 2019 at 5:37	comment	added	reuns		See en.wikipedia.org/wiki/Dirichlet_series#Abscissa_of_convergence if $\sum_{n=1}^\infty\frac{a(n)}{n^{s_0}}$ converges then $$\sum_{n=1}^\infty\frac{a(n)}{n^s}= \lim_{N\to \infty} N^{s_0-s} (\sum_{n=1}^N a(n) n^{-s_0}) + \sum_{n=1}^{N-1} (\sum_{m=1}^n a(m)m^{-s_0}) (n^{s_0-s}-(n+1)^{s_0-s})$$ converges and is analytic for $\Re(s) > \Re(s_0)$ and where it is meromorphic it has no poles on $\Re(s_0)$. The converse is very specific to $\zeta(s)$ and follows from the same Tauberian theorems as in the proof of the PNT.
Sep 18, 2019 at 23:15	history	rollback	Yemon Choi		Rollback to Revision 2
S Sep 18, 2019 at 22:41	history	suggested	user142929	CC BY-SA 4.0	Feel free to reject my edit: improved minor aspects of the post and added the tags (analytic-continuation) and (dirichlet-series)
Sep 18, 2019 at 21:36	review	Suggested edits
S Sep 18, 2019 at 22:41
Sep 18, 2019 at 17:29	answer	added	Wojowu		timeline score: 7
Sep 18, 2019 at 17:04	answer	added	David E Speyer		timeline score: 3
Sep 18, 2019 at 15:36	comment	added	Conrad		where did you hear that?
Sep 18, 2019 at 14:40	review	Close votes
Sep 30, 2019 at 3:05
Sep 18, 2019 at 14:17	history	edited	Rafik1	CC BY-SA 4.0	added 14 characters in body
Sep 18, 2019 at 14:15	review	First posts
Sep 18, 2019 at 15:12
Sep 18, 2019 at 14:11	history	asked	Rafik1	CC BY-SA 4.0