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Apparently, a(n+1) is the number of compositions n=p(1)+p(2)+...+p(m) with p(1)=1 and p(k) <= 7*p(k+1) Sagittarian Milky Way ( talk) 06:23, 20 December 2012 (UTC)
Hello,
suppose is an anisotropic quadratic form on a 2-dimensional vector space over a finite field of odd order. Let us denote 1-dimensional subspaces as points. will assume either square values on all non-zero vectors in a point, or non-square values on all such vectors. On how many points does it assume square values?
I know the answer is exactly half: (q+1)/2 , but what is the most elegant way to see this? I mean: is a coordinate-free proof possible?
Many thanks, Evilbu ( talk) 09:56, 20 December 2012 (UTC)
I'm trying to solve an equation of this form for x: I already know that the xe^x term makes this pretty much impossible to do in closed form, because the inverse of that is the Lambert W function. Is there a good numerical approach outside of Newton's method? Is there some way to quickly approximate a solution for the initial guess? The solution is going to be evaluated very quickly in a control loop on an embedded system, so I'm trying to simplify and optimize things as much as possible. I doubt the constants are related in a useful way to take advantadge of any special cases of the form, but let me know if you want me to post the (rather ugly) formulas for them. 209.131.76.183 ( talk) 21:05, 20 December 2012 (UTC)
I recently ordered a book about the Riemann Zeta Function from Cambridge and it talks of finding the Riemann Zeta Function of the empty set. However it does not go into detail, how would you do this? And what would the Riemann Zeta function of the empty set? — Preceding unsigned comment added by 86.140.200.90 ( talk) 21:06, 20 December 2012 (UTC)
Mathematics desk | ||
---|---|---|
< December 19 | << Nov | December | Jan >> | Current desk > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Apparently, a(n+1) is the number of compositions n=p(1)+p(2)+...+p(m) with p(1)=1 and p(k) <= 7*p(k+1) Sagittarian Milky Way ( talk) 06:23, 20 December 2012 (UTC)
Hello,
suppose is an anisotropic quadratic form on a 2-dimensional vector space over a finite field of odd order. Let us denote 1-dimensional subspaces as points. will assume either square values on all non-zero vectors in a point, or non-square values on all such vectors. On how many points does it assume square values?
I know the answer is exactly half: (q+1)/2 , but what is the most elegant way to see this? I mean: is a coordinate-free proof possible?
Many thanks, Evilbu ( talk) 09:56, 20 December 2012 (UTC)
I'm trying to solve an equation of this form for x: I already know that the xe^x term makes this pretty much impossible to do in closed form, because the inverse of that is the Lambert W function. Is there a good numerical approach outside of Newton's method? Is there some way to quickly approximate a solution for the initial guess? The solution is going to be evaluated very quickly in a control loop on an embedded system, so I'm trying to simplify and optimize things as much as possible. I doubt the constants are related in a useful way to take advantadge of any special cases of the form, but let me know if you want me to post the (rather ugly) formulas for them. 209.131.76.183 ( talk) 21:05, 20 December 2012 (UTC)
I recently ordered a book about the Riemann Zeta Function from Cambridge and it talks of finding the Riemann Zeta Function of the empty set. However it does not go into detail, how would you do this? And what would the Riemann Zeta function of the empty set? — Preceding unsigned comment added by 86.140.200.90 ( talk) 21:06, 20 December 2012 (UTC)