OFFSET
0,1
COMMENTS
Start from any complex number z=x+iy, not solution to zeta(z)=z, iterate the zeta function on z. If zeta_m(z)=zeta(zeta(....(z)..)) m times, has a limit when m grows, then this limit seems to always be the real number C = -0.2959050055752....
C is not only a real fixed point of zeta, but the only attractive fixed point of Riemann zeta on the real line. - Balarka Sen, Feb 21 2013
LINKS
Balarka Sen, Table of n, a(n) for n = 0..200
EXAMPLE
Let z=3+5I after 30 iterations : zeta_30(z)=-0.29590556499...-0.00000041029065...*I
MATHEMATICA
FindRoot[Zeta[z] - z, {z, 0}, WorkingPrecision -> 500] (* Balarka Sen, Feb 21 2013 *)
PROG
(PARI) -solve(x=-1, 0, zeta(x)-x) \\ Michel Marcus, May 05 2020
CROSSREFS
KEYWORD
AUTHOR
Benoit Cloitre, Apr 27 2002
STATUS
approved