02/25/2013, 10:48 AM
Thank you tommy1729 and bo198214, I understand 100% why such phenomena occurs.
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.
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.