Is Goodman's Conjecture true? | Manifold

Is Goodman's Conjecture true?

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Goodman's Conjecture is a statement about analytic multi-valued functions. According to the conjecture, if f(z) is a p-valent function with power series f(z) = b₁z¹ + b₂z² + ···, then the coefficients obey the inequality |bₙ| ≤ Σ [2k(n+p)!|bₖ|]/[(p-k)!(p+k)!(n-p-1)!(n²-k²)], where the sum ranges from k=1 to p.

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