Comment by handle584

1896 PNT is basically 1859 Riemann + a trig inequality.

1830 Dirichlet's result is qualitative only, it shows infinitude but not the asymptote in terms of the zeros for it predates Riemann.

To me this is the first substantial step after the 1896 PNT, and we really do not see much progress in the whole 20th century. Personally so far there are only two people worth mentioning,

- Euler, introduces the real zeta function and Euler product, establishes the functional equation at (half?) integers.

- Riemann, introduces complex analysis ideas to the zeta function.

And of course this result if it is true. This is first to penetrate the critical strip, which nobody had any idea how to approach for over a century and a half.