Is There a Topological or Geometrical Approach to the Riemann Hypothesis?

[narniaoff]

Hello dear forum members I wanted to know where are the research on the Riemann hypothesis , the latest advances ,who are the currently leading experts and is now known that mathematics it requires for its resolution

 

[CRGreathouse]

Hello dear forum members I wanted to know where are the research on the Riemann hypothesis , the latest advances ,who are the currently leading experts and is now known that mathematics it requires for its resolution

We don't appear to have enough mathematics developed for its resolution, no. The cutting edge research has been to show that a positive fraction (2/5?) of zeros must lie on the critical line and that almost all zeros are within epsilon of the critical line. There are also known zero-free regions near the boundary of the critical strip.

Many problems have been shown equivalent to the RH, notable (to me, at least) Robin's theorem. So far it seems like these other problems, though often elementary, are no easier to solve than the original. The 'direct approach' through analytic number theory seems the most likely resolution at the moment, though I doubt the solution will be found soon. (I'd love to be wrong there.)

 

[narniaoff]

thanks for your clear answers but i want to know is there a topological approach or geometrical approach of this problem

 

[CRGreathouse]

thanks for your clear answers but i want to know is there a topological approach or geometrical approach of this problem

None that I'm aware of, no.