Kouznetsov Wrote:Consider following Assumption:

There exist entire 1-periodic function such that

is also analytic tetration on base .

Then, function is not allowed to take values -2, -3, ..

being evaluated at elements of .

But does not need to be entire, it can also omit the values -2, -3 , ... as arguments.

For an entire function we would know that it can omit at most 1 value (Little Picard).

Edit: Oh I see now needs not to be entire, but can be continued being entire by if can be/is defined on the strip .