Leonardo

Thanks for all that. I'll have a look around some of your references.

That's very helpful, thanks. Just one more thing. You say it would be possible to prove RH by knowing enough about the position of primes. What would one have have to know about them? If one came up with a function that produced the primes would this allow RH to be proved? Or, would one then have to go on show that this function was equivalent to to R's zeta function? I take your point about 'handwaving'. Unfortunately the explicit formulae are over my head mathematically, which is why I have to ask what are probably daft questions. I haven't yet found a discussion of Riemann's zeros sufficiently simple that I can follow it. Pathetic really.

Thanks. I can't say I understand too much of that, but I get the general idea. The question about waves came from reading that the zeros are in some way like tuning forks, and that the interaction of their different frequencies in some way defines the primes. Is this roughly correct? In an in principle sort of way I'm trying to establish the relationship between the mechanism that generates the primes and the mechanism that generates the zeroes. Specifically, I'm wondering what the wave-related mathematics of Riemann's zeta function, the mechanism that generates the zeros, tells us about the nature of mechanism generating the primes. I'm also interested in what it would mean to prove Riemann's hypothesis. As far as I can see to do this we'd have to be able to predict the positions of the zeros to infinity. I have no idea what doing this would entail. However, because of the close link between zeros and primes I'm wondering whether being able to predict the position of the primes to infinity isn't almost as good as a proof of the hypothesis, as long as it could be shown that the mathematical mechanism generating the zeros and the primes are equivalent. Does this make sense? If it's all nonsense feel free to say so.

Hi folks I'm not a mathematician but I'd like to ask some simpleminded question about Riemann's hypothesis. It seems to me that the only way the hypothesis can be proved is by showing that the mathematical mechanism that generates the primes is exactly the same mechanism that generates the non-trivial zeros. Am I right about this? If I am then, bearing in mind the origins of the zeta function, would I also be right in thinking that a proof would require showing that the primes are generated or determined by an interaction of interacting sine waves akin to the process that generates the harmonics of a vibrating string? Thanks.