Zeta iterations Balarka Sen Junior Fellow Posts: 25 Threads: 7 Joined: Feb 2013 02/25/2013, 10:48 AM Thank you tommy1729 and bo198214, I understand 100% why such phenomena occurs. tommy1729 Wrote:How many fixpoints does zeta have actually ? As Mr. Helms says, there are infinitely many real fixed points of zeta occurs between the zeros but none of them is attractive since |zeta'(z0)| >> 1 for all the real negative zeta fixed points z0. Well, there is a positive fixed point (only one) but it's not attractive too and can easily be checked. Can one give an example of any complex fixed point of zeta with non zero imaginary part? I think I have read somewhere that it is not known if a complex one exists; but I could be wrong, you know. Gottfried Ultimate Fellow Posts: 880 Threads: 129 Joined: Aug 2007 02/26/2013, 09:49 AM Hi Balarka - I've remembered that there was also a question on Math Overflow for the iterated zeta, to which I've answered. Perhaps this is also of interest for you. See: http://mathoverflow.net/questions/72529/...a-function Gottfried Gottfried Helms, Kassel « Next Oldest | Next Newest »

 Possibly Related Threads… Thread Author Replies Views Last Post Qs on extension of continuous iterations from analytic functs to non-analytic Leo.W 18 1,803 09/18/2022, 09:37 PM Last Post: tommy1729 Apropos "fix"point: are the fractional iterations from there "fix" as well? Gottfried 12 1,043 07/19/2022, 03:18 AM Last Post: JmsNxn [note dump] Iterations and Actions MphLee 23 4,833 07/15/2022, 04:08 PM Last Post: MphLee Consistency in the composition of iterations Daniel 9 806 06/08/2022, 05:02 AM Last Post: JmsNxn Has anyone solved iterations of z+Γ(z)? Leo.W 5 2,314 01/07/2022, 08:15 AM Last Post: JmsNxn [MSE] Shape of orbit of iterations with base b on Shell-Thron-region Gottfried 14 22,540 12/13/2019, 02:33 PM Last Post: Ember Edison Math overflow question on fractional exponential iterations sheldonison 4 10,876 04/01/2018, 03:09 AM Last Post: JmsNxn Periodic analytic iterations by Riemann mapping tommy1729 1 5,258 03/05/2016, 10:07 PM Last Post: tommy1729 Limit of mean of Iterations of f(x)=(ln(x);x>0,ln(-x) x<0) =-Omega constant for all x Ivars 10 25,607 03/29/2015, 08:02 PM Last Post: tommy1729 zeta and sinh tommy1729 0 3,926 05/30/2011, 12:07 PM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)