# Freddie Manners

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## Registered User

 Name Freddie Manners Member for 1 year Seen May 18 at 21:12 Website Location Age
 Apr13 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. Apr13 revised Is there a “right” proof of Riemann’s Theta Relation?added 12 characters in body Apr12 asked Is there a “right” proof of Riemann’s Theta Relation? Apr9 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. Mar22 awarded ● Citizen Patrol Mar22 awarded ● Critic Mar22 awarded ● Commentator Mar22 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](mathoverflow.net/questions/91657/…). (3) has a very different flavour. It might be related to expansion in $SL_2$. Mar21 comment Joint (close to uniform) distribution in finite fieldsI 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. Mar21 revised Joint (close to uniform) distribution in finite fieldsdeleted 48 characters in body Mar21 revised Joint (close to uniform) distribution in finite fieldsadded 192 characters in body Mar21 comment Joint (close to uniform) distribution in finite fieldsKevin -- 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. Mar21 revised Joint (close to uniform) distribution in finite fieldstypo Mar21 answered Joint (close to uniform) distribution in finite fields Mar20 awarded ● Yearling Jan26 awarded ● Teacher Jan26 revised Question about the Hardy-Littlewood method (quite basic)added 7 characters in body; added 2 characters in body; edited body Jan26 answered Question about the Hardy-Littlewood method (quite basic)