Notice 0 < b^z < oo for finite complex z !
hence since b^z is unbounded to make f(z,1) b^z bounded we need f(z,1) going to 0 near the imaginary limits +/- oo i.
But f(z,1) b^z needs to be entire. And hence (by the above) f(z,1) cannot be entire.
Thus if f(z,1) b^z needs to be entire and f(z,1) goes to oo (f(z,1) goes to oo somewhere because its not entire ) ,we MUST conclude we need points z1 where b^z1 are 0.
But b^z is NEVER 0 in any strip.
This completes and clarfies the proof of post nr. 1.
I see that TPID 4 is still considered unproved in the open questions page.
I hope this post convinces everyone that I did indeed have proven TPID 4.
regards
tommy1729
hence since b^z is unbounded to make f(z,1) b^z bounded we need f(z,1) going to 0 near the imaginary limits +/- oo i.
But f(z,1) b^z needs to be entire. And hence (by the above) f(z,1) cannot be entire.
Thus if f(z,1) b^z needs to be entire and f(z,1) goes to oo (f(z,1) goes to oo somewhere because its not entire ) ,we MUST conclude we need points z1 where b^z1 are 0.
But b^z is NEVER 0 in any strip.
This completes and clarfies the proof of post nr. 1.
I see that TPID 4 is still considered unproved in the open questions page.
I hope this post convinces everyone that I did indeed have proven TPID 4.
regards
tommy1729
