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tag: number-theory -> nt.number-theory
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Rob Harron
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Nikita Sidorov
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vanvu
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Diophantine approximation

Let $P$ be a polynomial of fixed degree $d$ with integer coefficients of absolute values at most $n$. Assume that $P(\cos 2\pi/n)$ is no zero. Is there a lower bound for $|P(\cos 2\pi/n)|$ ? For instance, is this at least $n^{-C(d) }$ where $C(d)$ is some constant depending on $d$ ?