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May
4
comment Translation of Goldbach's 1742 letter to Euler
Brilliant. And we could all learn from his style...
May
4
accepted Translation of Goldbach's 1742 letter to Euler
May
4
awarded  Nice Question
May
3
awarded  Commentator
May
3
comment Translation of Goldbach's 1742 letter to Euler
Franz: that might be helpful?
May
3
comment Translation of Goldbach's 1742 letter to Euler
Ha! I wish. No, I'm preparing for a public lecture at the Radcliffe Institute.
May
3
comment Translation of Goldbach's 1742 letter to Euler
What is "the conjecture"? Something like every number $n$ being the sum of exactly $m$ "primes" for each $3 \leq m \leq n$, counting $1$ as prime? That's my guess just looking at the formulae in his letter. In the case $n = 2k + 2$ even and $m = 3$ it implies the usual Goldbach conjecture for $2k$, unless $2k - 1$ is prime.
May
3
comment Historical question concerning Jordan's theorem
Jim: I agree completely. I'd still like an actual reference to the argument I sketched above though, if there is one earlier than Tao's blog.
May
3
comment Historical question concerning Jordan's theorem
Yes indeed - and this paper has proved very useful indeed to many of us working in additive combinatorics recently. The paper also contains a proof in characteristic zero, but it is certainly a bit more complicated than the one I described above.
May
3
comment Translation of Goldbach's 1742 letter to Euler
Brilliant - now we just need someone who reads German to take a look at the footnote at the bottom of page 127.
May
3
asked Translation of Goldbach's 1742 letter to Euler
May
2
comment Historical question concerning Jordan's theorem
I should also point out that by $j(n)$ I think you mean the index of the biggest normal abelian subgroup of $A$; so your $j(n)$ is at most $F(n)!$, but they need not be the same.
May
2
comment Historical question concerning Jordan's theorem
Igor, I believe this issue is comprehensively despatched in this paper of M. J. Collins: On Jordan's theorem for complex linear groups. J. Group Theory 10 (2007), no. 4, 411--423. He evaluates $j(n)$ for all $n$ and shows that $(n+1)!$ is the truth for $n \geq 71$ (and not for $n = 70$). But my interest is more in finding the simplest argument that gives some bound.
May
2
awarded  Student
May
2
asked Historical question concerning Jordan's theorem
May
2
awarded  Critic
May
1
comment explicit big linearly independent sets
I think I agree!
May
1
answered explicit big linearly independent sets
Apr
29
answered Wanted: A constructive version of a theorem of Furstenberg and Weiss
Apr
27
comment Are There Primes of Every Hamming Weight?
Qiaochu: no, but I believe it would give one in principle, in the sense that there is no ineffectivity arising from a potential Siegel Zero. People I know who have done the kind of explicit calculations necessary to extract actual bounds from arguments like this attest that it is very painful, and the bounds are often pretty awful to boot.