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awarded | Enlightened |
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awarded | Nice Answer |
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answered | Random projection and finite fields |
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awarded | Scholar |
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Translation of Goldbach's 1742 letter to Euler
Brilliant. And we could all learn from his style... |
May
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accepted | Translation of Goldbach's 1742 letter to Euler |
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awarded | Nice Question |
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awarded | Commentator |
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Translation of Goldbach's 1742 letter to Euler
Franz: that might be helpful? |
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Translation of Goldbach's 1742 letter to Euler
Ha! I wish. No, I'm preparing for a public lecture at the Radcliffe Institute. |
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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. |
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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. |
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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. |
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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. |
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asked | Translation of Goldbach's 1742 letter to Euler |
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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. |
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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. |
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awarded | Student |
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asked | Historical question concerning Jordan's theorem |
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awarded | Critic |