Timeline for zeros of a complex function defined by integers

8 events

when toggle format	what		by	license	comment
Oct 28, 2017 at 5:51	answer	added	sku		timeline score: 1
Oct 20, 2017 at 18:09	answer	added	Stopple		timeline score: 3
Oct 19, 2017 at 22:37	comment	added	reuns		If you want an easier question forget about strictly increasing sequences of integers and construct analogs of $\frac{-\zeta'(s)}{\zeta(s)} = \sum_{n=1}^\infty \frac{\Lambda(n) }{n^{s}} =\sum_{n=2}^\infty \frac{\psi(n+\frac12)-\psi(n-\frac12)}{n^{s}}$ $=\sum_{n=2}^\infty \frac{1- \sum_\rho \frac{(n+\frac12)^\rho-(n-\frac12)^\rho}{\rho}}{n^{s}}$ where $\rho$ are the non-trivial and trivial zeros
Oct 19, 2017 at 22:25	answer	added	Igor Rivin		timeline score: 0
Oct 18, 2017 at 16:57	comment	added	hyportnex		@Fedor_Petrov I left that important detail out intentionally, I just wanted to know if it is possible at all that kind of distribution of zeros for some integer sequence. This seems to be an "easier" question than the Riemann hypothesis with specific $c=\frac{1}{2}$ and $\textbf{a} = 1,2,3,...$ . If assuming meromophy helps, so be it, whatever works (an engineer's view of the problem)!
Oct 18, 2017 at 14:11	comment	added	Fedor Petrov		In general this converges for $\Re z>1$. Do we consider a meromorphic continuation of this function, or what?
Oct 18, 2017 at 12:58	review	First posts
Oct 18, 2017 at 13:08
Oct 18, 2017 at 12:54	history	asked	hyportnex	CC BY-SA 3.0