An extremal problem for the geometric mean of polynomials

Beller, E.; Newman, D. J.

doi:10.1090/S0002-9939-1973-0316686-X

An extremal problem for the geometric mean of polynomials
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by E. Beller and D. J. Newman PDF

Proc. Amer. Math. Soc. 39 (1973), 313-317 Request permission

Abstract:

Let ${M_{0,n}}$ be the maximum of the geometric mean of all $n$th degree polynomials ${\sum ^n}{a_k}{e^{ikt}}$ which satisfy $|{a_k}| = 1,k = 0,1, \cdots ,n$. We show the existence of certain polynomials ${R_n}$ whose geometric mean is asymptotic to $\surd n$, thus proving that ${M_{0,n}}$ is itself asymptotic to $\surd n$.

References

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