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Dans cet article nous donnons des minorations de la mesure de Mahler des polynômes totalement positifs et totalement réels. Ces résultats sont supérieurs à ceux obtenus par A. Schinzel, M. J. Bertin et V. Flammang.
Introduction. In this note we use the following standard notations: π(x) is the number of primes not exceeding x, while .
The best known inequalities involving the function π(x) are the ones obtained in [6] by B. Rosser and L. Schoenfeld:
(1) x/(log x - 1/2) < π(x) for x ≥ 67
(2) x/(log x - 3/2) > π(x) for .
The proof of the above inequalities is not elementary and is based on the first 25 000 zeros of the Riemann function ξ(s) obtained by D. H. Lehmer [4]. Then Rosser, Yohe and Schoenfeld...
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