Speculations on the Riemann Hypothesis.
No, I don't have an answer to the hypothesis. But I do have some ideas about how to look at the problem differently. It bothers me that the zeros don't have a recognizable pattern beyond the 'repelling each other' characteristic so I suspect they could be improved for lack of a better word.
One more speculation is to go back to the idea of the primes being the results of the mold produced by the equations
- Could a zeta function be created for each of the separate groups of primes?
- Would the separate functions deliver the same zeros and would they lie on the same critical line?
- Could zeta functions be created for the other curves for the different combinations?
- Where would their zeros lie?
(6n + 1) * (6m - 1)
(6n - 1) * (6m + 1)
and
(6n – 1) * (6m - 1)
(6n + 1) * (6m + 1)
If you can buy into the idea that the prime numbers are the null result of these simple equations, then you might be able to tackle the Riemann Hypothesis by looking more closely at these equations. For example, if you could develop a zeta function for the 6n-1 primes, one possible solution is that their zeros would lie on a line at +0.16667 since the zero of (6a+1) * (6b-1) is 1/6. Similarly, the zeros for the 6n+1 primes would lie on a line at +0.333 since these primes are created from two equations, each with a zero of 1/6. Added up they come to the 0.5 of Riemann.
