hydro ha scritto:Non credo che gli esperti del settore ritengano di essere sulla buona strada. E' da più di un secolo che vengono proposti approcci nuovi, ma l'entusiasmo fa presto a passare...
Giusto per citare Terence Tao alla domanda "Stai cercando di risolvere l'ipotesi di Riemann?"
You know you can't really call your shots in mathematics. Some problems, the tools are not there. It doesn't matter how smart or quick you are. The analogy I have is like climbing, if you want to climb a cliff that's 10 high you can probably do it with the right tools and equipment, but you know if it's a sheer cliff face, you know, a mile high and there's no handholds whatsoever, you know just forget it. It doesn't matter how strong you are or whatever, you have to wait until there's some sort of breakthrough, like some opening occurs like halfway through halfway up the cliff and now you have some easier sub-goal. You know there's some speculation, there's some possible ways to attack the conjecture, but nothing is really promising currently.
ElementareWatson ha scritto:dan95 ha scritto: $ \Lambda \geq 0 $ (Terence Tao e Rodgers). Chiaramente per dimostrare l'ipotesi di Riemann è sufficiente verificare che $ H_0(z) $ non ha zeri reali ovvero che $ \Lambda \leq 0 $.
Non capisco, quindi si è vicini alla sua soluzione?
dan95 ha scritto:Diciamo che stiamo sulla buona strada, non mi viene da dire sulla giusta via, tuttavia questo approccio ha dato tante soddisfazioni fino adesso... e poi se lo segue Terry...
Sempre citando Terence Tao nel suo blog
https://terrytao.wordpress.com/2018/01/19/the-de-bruijn-newman-constant-is-non-negativ/ dice:
The following analogy (involving functions with just two zeroes, rather than an infinite number of zeroes) may help clarify the relation between this result and the Riemann hypothesis (and in particular why this result does not make the Riemann hypothesis any easier to prove, in fact it confirms the delicate nature of that hypothesis). Suppose one had a quadratic polynomial \(P\) of the form \(P(z)=z^2+ \Lambda \), where \( \Lambda \) was an unknown real constant. Suppose that one was for some reason interested in the analogue of the “Riemann hypothesis” for \(P\), namely that all the zeroes of \(P\) are real. A priori, there are three scenarios:
- (Riemann hypothesis false) \( \Lambda > 0 \), and \(P\) has zeroes \( \pm i \left| \Lambda \right|^{1/2} \) off the real axis.
- (Riemann hypothesis true, but barely so) \(\Lambda = 0 \), and both zeros of \(P\) are on the real axis; however, any slight perturbation of \( \Lambda \) in the positive direction would move zeroes off the real axis.
- (Riemann hypothesis true, with room to spare) \( \Lambda < 0 \), and both zeroes of \(P\) are on the real axis. Furthermore, any slight perturbation of \(P\) will also have both zeroes on the real axis.
The analogue of our result in this case is that \( \Lambda \geq 0 \), thus ruling out the third of the three scenarios here. In this simple example in which only two zeroes are involved, one can think of the inequality \( \Lambda \geq 0 \) as asserting that if the zeroes of \(P\) are real, then they must be repeated. In our result (in which there are an infinity of zeroes, that become increasingly dense near infinity), and in view of the convergence to local equilibrium properties of (3), the analogous assertion is that if the zeroes of \(H_0\) are real, then they do not behave locally as if they were in arithmetic progression.