tommy's group addition isomo conjecture - Printable Version +- Tetration Forum (https://tetrationforum.org) +-- Forum: Tetration and Related Topics (https://tetrationforum.org/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://tetrationforum.org/forumdisplay.php?fid=3) +--- Thread: tommy's group addition isomo conjecture (/showthread.php?tid=1640)

tommy's group addition isomo conjecture - tommy1729 - 09/15/2022 Let f(z) be an analytic function. let z1 , z2 be complex numbers of the form a^2 + b^2 i  and c^2 + d^2 i  such that Re ln(z1 + z2) =< ln (sqrt(2)) Let z_0 not be a fixpoint or cyclic point or singularity or pole of f(z). and let f^[z1 + z2](z_0) = f^[w](z_0) = f^[z_1](f^[z_2](z_0)) =   f^[z_2](f^[z_1](z_0)) For all z1,z2 such that z1 + z2 = w. Let s = g^2 + h^2 i Also let f^[s](z_0) be injective for all complex 0 =< s =< w. then  f^[s](z_0) is analytic in s if 0 =< s =< w. (the inequalities refer to the modulus comparisons) Regards tommy1729 RE: tommy's group addition isomo conjecture - tommy1729 - 09/16/2022 related : https://math.eretrandre.org/tetrationforum/showthread.php?tid=1639 https://math.eretrandre.org/tetrationforum/showthread.php?tid=1641