This question might be more suitable for http://math.stackexchange.com. I'm not sure about the differences between that website and this website (http://mathoverflow.net), so I'll try it here first.

All the zeros of the Riemann Zeta function on the complex plain are located either on the $[a+0i]$ line (known as *trivial zeros*), or between the $[0+ti]$ line and the $[1+ti]$ line (known as *non-trivial zeros*):

My question is with regards to the following facts:

I assume that none of them has been refuted, but has any of them been proved?

There is a finite number of

**non-trivial zeros**that are**not**located on the $[\frac{1}{2}+ti]$ line.There is a line in the form $[a+ti]$ with $0<a<1$, on which there is a finite number of zeros.

Thanks

notresolve RH), but that's just a logical misinterpretation of yours I suppose. Second, I can understand why proving the first fact might resolve RH (although it still requires an explanation). But why would proving the second fact resolve RH? If there is one such line (or even an infinite number of such lines), there can still be non-trivial zeros on other lines. $\endgroup$1more comment