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Mathematics professor at Cambridge
Feb
1 |
comment |
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 |
comment |
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 |
Jan
15 |
comment |
Improving a sequence of 1s and -1s
Quick question: does the set of 1s in a quasiperiodic sequence have to have a well-defined density? I keep trying to find a counterexample and I keep failing. |
Jan
15 |
awarded | Nice Question |
Jan
15 |
comment |
Has mathoverflow yet led to mathematical breakthroughs?
Apologies if I have asked the question in the wrong place -- meta isn't where it should be in my consciousness but I'll put it there now. |