This is an announcement for the paper "Some polynomial versions of cotype and applications" by Danie Carando, Andreas Defant, and Pablo Sevilla-Peris. Abstract: We introduce non-linear versions of the classical cotype of Banach spaces. We show that spaces with l.u.st and cotype, and that spaces having Fourier cotype enjoy our non-linear cotype. We apply these concepts to get results on convergence of vector-valued power series in infinite many variables and on $\ell_{1}$-multipliers of vector-valued Dirichlet series. Finally we introduce cotype with respect to indexing sets, an idea that includes our previous definitions. Archive classification: math.FA Submitted from: psevilla@mat.upv.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1503.00850 or http://arXiv.org/abs/1503.00850