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).