For electron-electron interactions in two-dimensional electronic systems the technique proposed by Singwi, Tosi, Land, and Sjolander (STLS) has been very promising. In this work, after showing the asymptotic behavior of the STLS local held correction we propose a simple expression for the local-held correction that contains two fitting parameters which are smoothly varying functions of the electronic density. The agreement of the fitting for the pair correlation function is remarkable. It further leads to an expression for the dielectric function which can be useful for applications. Finally, to assess the accuracy of the STLS technique, especially at low electronic densities we compare the STLS results with the available quantum Monte Carlo data.