Goodman's conjecture
Goodman's conjecture on the coefficients of multivalent functions was proposed in complex analysis in 1948 by Adolph Winkler Goodman, an American mathematician. Formulation 
Let  be a -valent function. The conjecture claims the following coefficients hold:

Partial results 
It's known that when , the conjecture is true for functions of the form  where  is a polynomial and  is univalent. External sources 

Complex analysis
Conjectures