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Oct 20, 2017 at 22:50 comment added hyportnex You are right! This has its zeros at two lines parallel with the imag axis, one at $c \approx 0.405$ and the other at $c \approx -0.202$. So then I should rephrase my question: could you find a sequence so that its zeros are only either on the negative real axis and/or a single line parallel with the imag axis on the RHS?
Oct 20, 2017 at 20:30 comment added Stopple @hyportnex see revision.
Oct 20, 2017 at 20:29 history edited Stopple CC BY-SA 3.0
added nontrivial example
Oct 20, 2017 at 19:35 comment added hyportnex This is all true but what about a function having zeros that are on the right half plane $\Re[z]>0$ (have positive real parts) as I was asking in my question admittedly with some tortured grammar.
Oct 20, 2017 at 18:09 history answered Stopple CC BY-SA 3.0