Timeline for Characterizing positivity of formal group laws
Current License: CC BY-SA 3.0
14 events
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| Feb 15, 2018 at 7:29 | history | edited | Pietro Majer | CC BY-SA 3.0 |
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| Feb 12, 2018 at 20:23 | comment | added | Pietro Majer | Yes, indeed it can also be proven by induction from the formula I wrote, integrating by parts several times | |
| Feb 12, 2018 at 19:36 | comment | added | Tom Copeland | @PietroMajer, your feelings about the integrality of the coefficients of $\psi$ are indeed true. See my answer/comments. | |
| Feb 10, 2018 at 0:10 | comment | added | Jair Taylor | This all makes sense to me. I think it should lead to a combinatorial interpretation as well. I'll need to think about that. | |
| Feb 10, 2018 at 0:09 | history | bounty ended | Jair Taylor | ||
| Feb 10, 2018 at 0:09 | vote | accept | Jair Taylor | ||
| Feb 9, 2018 at 23:08 | comment | added | Pietro Majer | Computing the first terms of the sequence I got, $\psi_0=x$, $\psi_1=\phi$, $\psi_2=\phi(\phi'-t_1)$, $\psi_3=\phi({\phi'}^2+\phi''\phi-t_2-3t_1\phi''+3t_1t_2)$. The feeling is that $\psi_n$ could be always a polynomial with integer coefficients in $\phi,\phi',\dots,\phi^{(n-1) }$. | |
| Feb 9, 2018 at 11:28 | history | edited | Pietro Majer | CC BY-SA 3.0 |
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| Feb 9, 2018 at 5:39 | comment | added | Jair Taylor | Ah, I see! That makes sense, thanks! It would seem this is proven. Allow me to think through the implications of this a bit and then I'll accept your answer. | |
| Feb 9, 2018 at 5:37 | comment | added | Pietro Majer | Yes, of course, but by the complete induction hypothesis $\psi_j=\phi \chi_j$ for $1\le j<n$, with $\chi_j$ a formal power series with positive coefficients, and there are at least two factors $\psi_j$ in each product, since it's on $s\in\alpha$ with $|\alpha|>1$... | |
| Feb 9, 2018 at 5:13 | comment | added | Jair Taylor | These computations look good to me. But why does the last equation have positive coefficients? The $\phi^{-2}(t)$ may have negative coefficients, no? | |
| Feb 9, 2018 at 4:58 | history | edited | Pietro Majer | CC BY-SA 3.0 |
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| Feb 9, 2018 at 4:26 | history | edited | Pietro Majer | CC BY-SA 3.0 |
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| Feb 9, 2018 at 4:21 | history | answered | Pietro Majer | CC BY-SA 3.0 |