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For the polynomials $\\sigma_{N}^{(c)} (x) := \\sum_{n=0}^{N-1} t_n^{(c)} e^{2\\pi i n x}$, we have proved in [18] that the uniform norm $\\|\\sigma_N^{(c)}\\|_\\infty$ behaves like $N^{\\gamma(c)}$ and the best exponent $\\gamma(c)$ is computed. 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For the polynomials $\\sigma_{N}^{(c)} (x) := \\sum_{n=0}^{N-1} t_n^{(c)} e^{2\\pi i n x}$, we have proved in [18] that the uniform norm $\\|\\sigma_N^{(c)}\\|_\\infty$ behaves like $N^{\\gamma(c)}$ and the best exponent $\\gamma(c)$ is computed. 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