  Recently, in paper published in the Annals of Mathematics, it was shown that
the Bohnenblust-Hille inequality for (complex) homogeneous polynomials is
hypercontractive. However, and to the best of our knowledge, there is no result
providing (nontrivial) lower bounds for the optimal constants for n-homogeneous
polynomials (n > 2). In this short note we provide lower bounds for these
famous constants.
