Report on some papers related to the function R (s) found by Siegel in Riemann's posthumous papers

In a letter to Weierstrass Riemann asserted that the number N₀ (T) of zeros of (s) on the critical line to height T is approximately equal to the total number of zeros to this height N (T). Siegel studied some posthumous papers of Riemann trying to find a proof of this. He found a function R (s) whose zeros are related to the zeros of the function (s). Siegel concluded that Riemann's papers contained no ideas for a proof of his assertion, connected the position of the zeros of R (s) with the position of the zeros of (s) and asked about the position of the zeros of R (s). This paper is a summary of several papers that we will soon upload to arXiv, in which we try to answer Siegel's question about the position of the zeros of R (s). The articles contain also improvements on Siegel's results and also other possible ways to prove Riemann's assertion, but without achieving this goal.