1,170 reputation
922
bio website www-personal.umich.edu/~gkopp
location University of Michigan
age 26
visits member for 4 years, 4 months
seen 2 days ago
I am a math graduate student at the University of Michigan. I graduated from the University of Chicago in 2011.

Aug
12
awarded  Yearling
Jul
2
awarded  Curious
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
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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