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Does anyone know any upper bounds or known results on LOWER BOUNDS for binary forms i.e.

if you have F(X,Y)=$X^n+YX^{n-1}+Y^2X^{n-2}+...+XY^{n-1}+Y^{n}$, I need to find a lower bound

for F interms of Y for e.g. $|F(X,Y)| \geq Y^n$ (not saying this is true).

I have found upper bounds in the literature extensively but no lower bounds yet.

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    How does this differ from the question http://math.stackexchange.com/questions/139119/binary-forms-of-degree-n you just asked a few hours ago?2012-05-01
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    Gerry Myerson: I've flagged that question for deletion, as it was causing confusinon.2012-05-01
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    Are $X,Y$ taking real numbers?2012-05-01
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    wxu: Yes they're real numbers2012-05-01
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    Okay, what is the bound for $n=1$, i.e., $|X+Y|$, is zero?2012-05-01
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    Notice for $n$ odd choosing $X=-Y$ gives $F(X,Y)=0$.2012-05-01
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    wxu: good point, I'm particularly interested in the case where n=4.2012-05-01
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    wxu: I suppose it doesn't make much sense for odd n. In the case n=2 it's 3/4Y^22012-05-01
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    So for $n=4$, you only need to figure out the minimal values of $|t^4+t^3+t^2+t+1|$, where $t\in \mathbb{R}$.2012-05-01
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    wxu: I'm having trouble seeing why this is. If I found the minimal values of that function, how does that translate into a lower bound in terms of Y?2012-05-01
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    $F(X,Y)=F(X/Y,1)Y^n$, write $t=X/Y$...2012-05-01
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    anon: wow great, thank you guys.2012-05-01
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    Instead of flagging the previous version for deletion, it would have been better just to edit it.2012-05-01

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