Petites valeurs de la fonction d'Euler

AbstractLet φ be the Euler's function. A question of Rosser and Schoenfeld is answered, showing that there exists infinitely many n such that nφ(n) > ey log log n, where γ is the Euler's constant. More precisely, if Nk is the product of the first k primes, it is proved that, under the Riemann's hypothesis, Nkφ(Nk) > ey log log Nk holds for any k ≥ 2, and, if the Riemann's hypothesis is false this inequality holds for infinitely many k, and is false for infinitely many k