Note on the asymptotic of the auxiliary function

To define an explicit regions without zeros of R (s), in a previous paper we obtained an approximation to R (s) of type f (s) (1+U) with |U|< 1. But this U do not tend to zero when t+. In the present paper we get an approximation of the form f (s) (1+o (t) ). We precise here Siegel's result, following his reasoning. This is essential to get the last Theorems in Siegel's paper about R (s).