bio | website | gowers.wordpress.com |
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visits | member for | 5 years, 9 months |
seen | May 22 at 10:59 | |
stats | profile views | 32,642 |
Mathematics professor at Cambridge
Feb 26 |
answered | Different ways of proving that two sets are equal |
Feb 26 |
awarded | Nice Question |
Feb 26 |
comment |
Heuristic argument for the prime number theorem?
That may indeed be exactly what I am looking for. I'll have to digest it carefully to see. |
Feb 26 |
asked | Heuristic argument for the prime number theorem? |
Feb 25 |
revised |
Definition of longest common subsequences
Changed "it's" to "its" |
Feb 25 |
answered | Various concepts of “closure” or “completion” in mathematics |
Feb 24 |
comment |
Value of “of course” in the mathematical literature
Was it by any chance me? Probably not, but it is something I have often said. But I didn't think it up for myself -- I got it from David Preiss. It's useful not just for evaluating the work of others, but also one's own work. That is, if you've just written a proof of something but don't feel quite secure about it, look for the bits where you didn't give full detail. |
Feb 20 |
answered | Similarly Ordered |
Feb 20 |
answered | Non-principal ultrafilters on ω |
Feb 16 |
answered | Problem equivalent to “largest square in a cube” |
Feb 8 |
awarded | Nice Question |
Feb 7 |
comment |
alternative construction of the quotient group
I don't claim it's a good way of doing things, but one could (in desperation) argue that here one is defining quotients in just one situation (what you need to define a group in terms of generators and relations) and getting all quotients out of it. But I wouldn't want to go to the wall on this one ... |
Feb 7 |
answered | alternative construction of the quotient group |
Feb 5 |
answered | Yet more on distortion |
Feb 3 |
asked | Is this a well-known probabilistic model? |
Feb 3 |
comment |
Why does the Riemann zeta function have non-trivial zeros?
That is a very useful comment -- thanks! |
Feb 2 |
comment |
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 |
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. |