Some estimates of the integral $\int_0^{2\pi}{\text Log}\,|P(e^{i\theta})|(2\pi)^{-1}\,d\theta$

Stojan Radenovi\'c

Abstract: We investigate some estimates of the integral $\int_0^{2\pi}\text{Log}\,|P(e^{i\th})|\df{d\th}{2\pi}$, if the polynomial $P(z)$ has a concentration at low degrees measured by the $l_p$-norm, $1\le p\le 2$. We also obtain better estimates for some concentrations than those obtained in [1].

Classification (MSC2000): 30C10

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