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Apr
13
comment Is there a “right” proof of Riemann's Theta Relation?
@J. Martel: I have to confess I started to get a bit out of my algebraic depth with the later (adelic) stuff in Tata III, so haven't yet managed to get a working understanding of Thm 7.4, but will persevere. Possibly I should just try to figure out what that result is saying in the Euclidean case. @Jeff: That would be great! @Everyone: the equation for $x_1$ in Mumford looks like it must be a typo; corrected in the above.
Apr
13
revised Is there a “right” proof of Riemann's Theta Relation?
added 12 characters in body
Apr
12
asked Is there a “right” proof of Riemann's Theta Relation?
Apr
9
comment Minimal size of subsets $A,B$ in a finite group $G$ such that $AB=G$
So, the strategy when A = H is a subgroup generalizes to A being your favorite set with $|A A^{-1}| = O(|A|)$, by a similar packing argument (if you accept a constant factor at the end). The aim is then to find such a set with $|A| \approx \sqrt{N}$. This gives rise to the cyclic example above, and should do what Colin Reid wants for nilpotent groups (see above). I don't know Whether you could use something like this to avoid the use of CFSG in the general case.
Mar
22
awarded  Citizen Patrol
Mar
22
awarded  Critic
Mar
22
awarded  Commentator
Mar
22
comment More expanders?
My guess is that (1) and (2) are doomed not to expand because they are "too abelian", or "too nilpotent". So for (1), a set like $\{\pm g^{n} : 0 \le n \le N \}$ for $N$ large (but small compared to $p$) is likely to contradict expansion. Something similar should work in (2), considering a set of bounded length words on both your generators. I think this is closely related to this MO question. (3) has a very different flavour. It might be related to expansion in $SL_2$.
Mar
21
comment Joint (close to uniform) distribution in finite fields
I think that's right -- third edit lucky. I think the $L^2$ result should give $\varepsilon$ up to a (basically) constant factor like $k / (k - 1)$, meaning the $L^1$ result should go as $k \varepsilon$ times some constant factor; i.e. this hasn't made too much difference to the conclusion.
Mar
21
revised Joint (close to uniform) distribution in finite fields
deleted 48 characters in body
Mar
21
revised Joint (close to uniform) distribution in finite fields
added 192 characters in body
Mar
21
comment Joint (close to uniform) distribution in finite fields
Kevin -- thanks! You're absolutely right, and that means there's also an $\varepsilon^2$ that needs tracing through the argument. I'll fix this now and see what I get.
Mar
21
revised Joint (close to uniform) distribution in finite fields
typo
Mar
21
answered Joint (close to uniform) distribution in finite fields
Mar
20
awarded  Yearling
Jan
26
awarded  Teacher
Jan
26
revised Question about the Hardy-Littlewood method (quite basic)
added 7 characters in body; added 2 characters in body; edited body
Jan
26
answered Question about the Hardy-Littlewood method (quite basic)
Jun
20
comment The space of lattices and modular forms of weight 1/2
@David Loeffler: fixed (I think), thanks.
Jun
20
revised The space of lattices and modular forms of weight 1/2
added 5 characters in body