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Nous prouvons qu'il existe des constantes absolues ci > 0 et c 2 > 0 telles que pour tout {a 0 ,a 1 ,...,a n )⊂[1,M], 1 < M < exp(c 1 n 1/4 ), il existe b 0 ,b 1 ,...,b n ∈ {-1,0,1} tels que P(z) = n Σ j=0 b j a j z J a au moins c 2 n 1/4 changements de signe distincts dans ]0,1[. Cela ameliore et etend des resultats anterieurs de Bloch et Polya.

Extensions of the Bloch–Pólya theorem on the number of real zeros of polynomials