2024/06/10 by de Reyna, Juan Arias
#FOS: Mathematics #Number Theory (math.NT) #Primary 11M06 #Secondary 30D99
paper · doi:10.48550/arxiv.2406.06066
To define an explicit regions without zeros of \mathop\mathcal R(s), in a previous paper we obtained an approximation to \mathop\mathcal 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 \mathop\mathcal R(s).