Timeline for Algebraic function with extra condition, what can it be?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Feb 4, 2012 at 22:00 | comment | added | Will Sawin | I'm not sure I understand what you mean. Since constants are homogeneous of total degree $0$, if $x$ is similarly homogeneous, so is $(ax+b)/(cx+d)$. But ... is your function entire? If not, is it meromorphic? | |
| Feb 4, 2012 at 11:24 | comment | added | Per Alexandersson | @Will Sawin: But the rational linear transform must be homogeneous as well... | |
| Feb 3, 2012 at 7:22 | comment | added | Will Sawin | oh sorry. i meant a rational function of total degree zero like $\zeta_1^2\zeta_2^{-1}\zeta_3^{-1}$ | |
| Feb 2, 2012 at 22:09 | comment | added | Per Alexandersson | @Will Sawin: A polynomial of degree zero? That sounds very much like a constant... | |
| Feb 2, 2012 at 18:20 | comment | added | Will Sawin | well maybe not arbitrarily. But extremely. | |
| Feb 2, 2012 at 18:20 | comment | added | Will Sawin | If your function is allowed to have poles, this is false. Let $f$ be any rational linear transformation of the Riemann sphere that preserves the roots of unity, and let $g$ be a homogeneous polynomial of degree zero, then multiplying by $f\circ g$ will preserve all the properties given, and you can make your function arbitrarily complicated like this. | |
| Feb 2, 2012 at 17:59 | history | answered | Will Sawin | CC BY-SA 3.0 |