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The following paper seems to fully answer the question:
http://arxiv.org/pdf/1205.0846.pdf.
It follows from this paper that $P'(x)\le O_{\epsilon}(\log d)$ in the interval $[-1+\epsilon,1-\epsilon]$.
The following paper seems to fully answer the question:
http://arxiv.org/pdf/1205.0846.pdf.
It follows from this paper that $P'(x)\le O_{\epsilon}(\log d)$ in the interval $[-1+\epsilon,1-\epsilon]$.
The following paper seems to fully answer the question:
http://arxiv.org/pdf/1205.0846.pdf.
It follows from this paper that $P'(x)\le O_{\epsilon}(\log d)$ in the interval $[-1+\epsilon,1-\epsilon]$.
