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Mathematics professor at Cambridge
Feb 3 |
comment |
Why does the Riemann zeta function have non-trivial zeros?
That is a very useful comment -- thanks! |
Feb 2 |
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Why does the Riemann zeta function have non-trivial zeros?
That was another of the thoughts that lay behind my question. Somehow the fact that the distribution of primes can't be "better than random" feels like a fact that ought to have an elementary proof using some Parseval-like identity. I suspect the zeta function is sort of doing that (with a Mellin transform rather than a Fourier transform), but it doesn't appear to be saying something simple like, "That function has the same L_2 norm and trivially has L_2 norm at least the square root of n." |
Feb 1 |
awarded | Nice Question |
Feb 1 |
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Why does the Riemann zeta function have non-trivial zeros?
That is a very nice argument, but it also has a magic flavour to it, since you somehow manage to bootstrap a very small error (arising from the fact that $\psi_0(x)$ is discontinuous) into a much bigger one (that the error term in PNT must be more like a square root). But perhaps the bootstrapping is done by the functional equation rather than your argument. |
Feb 1 |
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Why does the Riemann zeta function have non-trivial zeros?
It's precisely this issue -- why the error term in PNT isn't absolutely tiny -- that I want to understand. E.g. to prove that π(x) does not approximate $Li(x)$ to within $latex x^{1/3}$, the obvious method is to point to the zeros on the critical line. So I'm going round in circles. With the help of the functional equation one can say that if there are no zeros on or to the right of the critical line then there are none at all, but I don't count that as an intuitive argument. |
Feb 1 |
revised |
Why does the Riemann zeta function have non-trivial zeros?
Added tag |
Feb 1 |
asked | Why does the Riemann zeta function have non-trivial zeros? |
Jan 26 |
awarded | Nice Answer |
Jan 23 |
awarded | Nice Answer |
Jan 22 |
comment |
Proving “almost all matrices over C are diagonalizable”.
Or you could simply upper-triangularize your matrix and do the same. |
Jan 22 |
answered | Switching Research Fields |
Jan 22 |
awarded | Nice Answer |
Jan 21 |
revised |
A random variable: is it a function or an equivalence class of functions?
added 994 characters in body |
Jan 21 |
answered | A random variable: is it a function or an equivalence class of functions? |
Jan 20 |
revised |
Experimental Mathematics
added 32 characters in body |
Jan 18 |
answered | Baire category theorem |
Jan 17 |
answered | Experimental Mathematics |
Jan 16 |
answered | Justifying a theory by a seemingly unrelated example |
Jan 15 |
answered | Nontrivial question about fibonacci numbers? |
Jan 15 |
awarded | Nice Question |