05/28/2011, 09:18 AM

(05/27/2011, 10:48 PM)tommy1729 Wrote: if there are 2m regular superfunctions f_i from one fixpoint , is it true that at least m of those can be chosen such that

f_i(z) = f_j(z + p_q(z) + Q) ??

where p_q(z) is a periodic function and Q is a constant.

Yes, first a (regular) superfunction is always undetermined by an x-axis shift, this is the role of Q.

Second if you have any two superfunctions f and g, then

(if g is suitably injective) is always a 1-periodic function, which follows from the definition of Abel and superfunction.