Jackson Walters

848 reputation

111

bio	website
	location	Blacksburg, VA
	age	22
visits	member for	1 year, 10 months
	seen	May 15 at 2:18
stats	profile views	118

I am an undergraduate at Virginia Tech double majoring in math and physics and minoring in computer science.

	848 reputation	bio	website		visits	member for	1 year, 10 months
111 badges		location	Blacksburg, VA		seen	May 15 at 2:18

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May 9	awarded	Caucus
Apr 21	revised	Trying to extend Vandermonde's formula to the case where m and n are not integers TeXified everything.
Apr 21	suggested	suggested edit on Trying to extend Vandermonde's formula to the case where m and n are not integers
Apr 11	accepted	$x \in \left[L,L\right] \Rightarrow tr(ad \, x)=0$
Apr 3	comment	$x \in \left[L,L\right] \Rightarrow tr(ad \, x)=0$ Why do we get to assume the Lie bracket is a commutator? Surely there are more general brackets.
Apr 3	asked	$x \in \left[L,L\right] \Rightarrow tr(ad \, x)=0$
Jan 16	accepted	What topological space do I obtain by gluing these edges?
Jan 12	comment	Möbius function sum $S(2,1;s)=\frac{1}{(1-2^{-s})\zeta(s)}$.
Jan 11	asked	What topological space do I obtain by gluing these edges?
Jan 7	awarded	Citizen Patrol
Dec 14	revised	Commutative Rings and Ideals added 2 characters in body
Dec 14	revised	Commutative Rings and Ideals subsets are indeed proper
Dec 14	answered	Commutative Rings and Ideals
Dec 12	revised	How do I explain 2 to the power of zero equals 1 to a child Texified the expressions.
Dec 12	suggested	suggested edit on How do I explain 2 to the power of zero equals 1 to a child
Dec 12	comment	Ideals of norm 2 in $\mathbb{Z}[\zeta_{n}]$ Great answer, thanks!
Dec 12	accepted	Ideals of norm 2 in $\mathbb{Z}[\zeta_{n}]$
Dec 12	comment	Ideals of norm 2 in $\mathbb{Z}[\zeta_{n}]$ This is a bit over my head as I haven't had a course in ANT yet, but I can more or less follow along. Does all of this imply that 2 being a generator for $(\mathbb{Z}/n\mathbb{Z})^{\times}$ is a necessary condition for $A$ to be an ideal of norm 2 in $\mathbb{Z}[\zeta_{n}]$?
Dec 12	comment	Ideals of norm 2 in $\mathbb{Z}[\zeta_{n}]$ I was assuming from the definition of Euclidean domain. The only ones I've read about are the norms on $\mathbb{Z}$, $\mathbb{Z}[i]$, $\mathbb{Z}[\omega]$, and $\mathbb{Z}[\zeta_{5}]$. The norm on $\mathbb{Z}[\zeta_{5}]$ that I linked to is significantly more complicated than the others. The computer program I've written was designed specifically for $\mathbb{Z}[\omega]$ and I already know there are no ideals of index 2 in $\mathbb{Z}[\zeta_{5}]$. I was just wondering if there was a quicker/more general way to answer this rather than brute force computation.
Dec 12	comment	Ideals of norm 2 in $\mathbb{Z}[\zeta_{n}]$ Pretty sure. I wrote a Euclidean algorithm to compute remainders in $\mathbb{Z}[\omega]$. One can prove that the the the number of representatives is finite. For a given ideal $(\beta)$ I can compute a list guaranteed to contain every representative. By removing all duplicates from the list ($a-b \in (\beta)$ means $a$ and $b$ are duplicates) I get a list of distinct coset representatives which tells me the index.