Let denote the set of algebraic polynomials of degree n with the real coefficients. Stein and Wpainger [1] proved thatwhere C n depends only on n. Later A. Carbery, S. Wainger and J. Wright (according to a communication obtained from I. R. Parissis), and Parissis [3] obtained the following sharp order estimate Now let denote the set of trigonometric polynomialswith real coefficients a k , b k . The main result of the paper is that with an effective bound on C n . Besides, an analog of a lemma, due to I. M. Vinogradov, is established, concerning the estimate of the measure of the set, where a polynomial is small, via the coefficients of the polynomial.
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