$\pi$-exponentials for generalized twisted ramified Witt vectors

Abstract

In this paper, we generalize Hazewinkel’s theory of twisted ramified Witt rings and then generalize $\pi$-exponentials defined by Pulita using newly defined Witt vectors. As an application,we determine the radii of convergence of some formal group exponentials.We also show that $p$-typical part of a theorem of R. Richard [Ric15] on the convergence of $\pi$-exponentials holds for these series and prove some overconvergence properties of related series.