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 $f(z)= \sum_^$ be a $p$-valent function. The conjecture claims the following coefficients hold:
$, b_n, \le \sum_^ \frac, b_k,$

Partial results

It's known that when $p=2,3$, the conjecture is true for functions of the form $P \circ \phi$ where $P$ is a polynomial and $\phi$ is univalent.

External sources

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*{{cite journal , doi=10.1090/S0002-9939-1995-1242085-7, title=On an identity related to multivalent functions , year=1995 , last1=Grinshpan , first1=A. Z. , journal=Proceedings of the American Mathematical Society , volume=123 , issue=4 , page=1199 , doi-access=free

Complex analysis
Conjectures