Abstract:
Generalized Chebyshev polynomials are introduced and studied in this paper. They are applied to obtain a lower bound for the $\sup$-norm on the closed interval for nonzero polynomials with integer coefficients of arbitrary degree.
Keywords:extremal properties of polynomials, Hilbert–Fekete theorem, integer algebraic numbers, asymptotic law of the distribution of primes, Eisenstein criterion for the irreducibility of polynomials.
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