Although there is a great deal of research on Riemann's two papers, there are yet some content and formulas not being studied thoroughly. The most typical example is the following formula

nobody has pointed out why Riemann gave it since 1932. This is Riemann's conclusion in his nachlass. Namely N(T)=N0(T). Please look athttps://arxiv.org/pdf/1508.02932v5.pdf