On recent strategies proposed for proving the Riemann hypothesis

Abstract

We comment on some apparently weak points in the novel strategies recently developed by various authors aiming at a proof of the Riemann hypothesis. After noting the existence of relevant previous papers where similar tools have been used, we refine some of these strategies. It is not clear at the moment if the problems we point out here can be resolved rigorously, and thus a proof of the RH be obtained, along the lines proposed. However, a specific suggestion of a procedure to overcome the encountered difficulties is made, what constitutes a step towards this goal.