bio | website | www-personal.umich.edu/~gkopp |
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location | University of Michigan | |
age | 25 | |
visits | member for | 3 years, 8 months |
seen | yesterday | |
stats | profile views | 1,131 |
I am a math graduate student at the University of Michigan. I graduated from the University of Chicago in 2011.
Nov 13 |
awarded | Good Question |
Nov 5 |
awarded | Popular Question |
Oct 21 |
comment |
Euclidean real quadratic fields
I'm not sure what you mean by "a single (or finitely many) Euclidean function(s)"; how do you tell whether two Euclidean functions for different number rings are the same or different? Anyway, this paper arxiv.org/abs/1106.0856 might interest you. |
Oct 21 |
comment |
Jokes in the sense of Littlewood: examples?
@Michael: I'm not quite sure what you're getting at. The $\lambda_i$ live in $\overline{K(x_{11}, x_{12}, \cdots, x_{nn})}$ but not in $K(x_{11}, x_{12}, \cdots, x_{nn})$, so that doesn't tell you anything downstairs. |
Oct 9 |
comment |
When is a Number Ring generated by its Norm-1 elements?
For a real quadratic field of discriminant $d$, the condition holds if and only if $\frac{d}{4}+1$ is a square, so, as you said, rarely. However, the relationship Bump mentions works for all real quadratic fields, if you phrase it as, "there's a natural bijection between the ideal classes of all orders $\mathcal{O}$ of $K$ and the hyperbolic conjugacy classes of ${\rm PSL}_2(\mathbb{Z})$ with eigenvalues in $K$." Your condition guarantees that the ideals of the max order $\mathcal{O}_K$ correspond to the conjugacy classes having the fundamental unit as an eigenvalue. |
Sep 4 |
revised |
Set of primes dividing polynomials and composition
added 216 characters in body |
Sep 4 |
answered | Set of primes dividing polynomials and composition |
Aug 12 |
awarded | Yearling |
Jul 28 |
comment |
Subgroups of finite index of fields
No. Consider finite fields. |
Jul 25 |
comment |
Class numbers of orders
Updated the answer. Thanks for pointing that out, David. |
Jul 25 |
revised |
Class numbers of orders
added 259 characters in body |
Jul 25 |
revised |
Class numbers of orders
deleted 1 characters in body |
Jul 25 |
answered | Class numbers of orders |
Jun 20 |
awarded | Autobiographer |
Jun 20 |
answered | Polynomials giving Lower Degree Elements in an Algebraic Number Field |
Apr 10 |
comment |
Irreducible Degrees and the Order of a Finite Group
Another interesting point about the Bump and Ginzburg paper is that it provides a combinatorial interpretation for the $a_g$ assuming the existence of an involution on $G$ with certain properties. |
Apr 10 |
comment |
Irreducible Degrees and the Order of a Finite Group
Bump and Ginzburg remark on page 4 of their paper "Generalized Frobenius-Schur Numbers" that the Mathieu group $M_{11}$ provide another example where some of the $a_g$ are negative (and that the observation goes back to Solomon and Thompson). @David, your example is smaller (order 1920 versus 7920), so maybe it is not well-known. |
Mar 8 |
awarded | Nice Answer |
Feb 27 |
comment |
Exercise in Milne's CFT notes
From a practical point of view, an easy way to check if you are right or wrong is to appeal to CM theory. In Mathematica, RootApproximant[KleinInvariantJ[Sqrt[-6]]] gives $1399+988\sqrt{2}$. The j-invariant generates the HCF, so Milne is right. |
Dec 29 |
awarded | Nice Answer |