3,866 reputation
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bio website math.lsa.umich.edu/~zieve
location University of Michigan
age
visits member for 1 year, 11 months
seen 16 mins ago

I am a professor at the University of Michigan. In 2013-2014 I am on leave from Michigan, and I am at Shing-Tung Yau's Mathematical Sciences Center attached to Tsinghua University.


1d
comment Weil's Riemann Hypothesis for dummies?
You might like to look into Stichtenoth's book "Algebraic function fields and codes", which gives a completely self-contained exposition of the Riemann hypothesis for curves and all material leading up to it. It is completely algebraic and non-geometric, but it does get to Weil's Riemann hypothesis very quickly starting from nothing.
1d
comment Weil's Riemann Hypothesis for dummies?
@Dustin: yes, see my answer.
1d
answered Weil's Riemann Hypothesis for dummies?
Jul
4
comment The equation $f(x)=f(a^n)^k$ always has a solution in $\mathbb{Q}$
The question was copied verbatim from the website Rodgrigo pointed to. It seems strange that the OP did not mention the question's source, or that a solution was given at that source.
Jul
2
awarded  Curious
Jun
29
comment Relations among the height of algebraic numbers
Related question: mathoverflow.net/questions/64643/…
Jun
29
comment Relations among the height of algebraic numbers
This is not possible unless you bound the degrees of a and b as well. The trace of $a+1$ is $\text{tr}(a)+\text{deg}(a)$.
Jun
18
comment Quadratic twist of curve defined over finite field
An elementary exposition of twists in the case of curves over finite fields is Proposition 5.2.8 of Stichtenoth's book "Algebraic Function Fields and Codes". The proof there is essentially Chebotarev's field-crossing argument, and makes the proof of the function field analogue of Chebotarev's density theorem seem quite natural, which might be helpful for thinking about the proof in the number field case.
Jun
5
revised Lagrange Interpolation and integer polynomials
added 196 characters in body
Jun
5
answered Lagrange Interpolation and integer polynomials
May
26
comment Enumerating certain types of permutation polynomials
I want to clarify that the current (7th) version of this question is internally inconsistent. For $q=3$ there are 31555584 permutations $f$ of $GF(q^3)$ which satisfy conditions (1) and (2). The OP's assertion that there are only 3852 such permutations is wrong. It appears that the OP did not compute these permutations, but got the number 3852 from the number of perfect matchings in the incidence graph of $PG(2,3)$. So the real question is to find the mistake in the OP's proof (given in version 7 of the question) that the number of such permutations equals the number of perfect matchings.
May
22
comment Maximal separable extension of $\mathbb F_q((t))$
@user76758: thanks for the correction. To salvage something of what I said, I just wanted to make the simple observation that the absolute Galois group of $\overline{\mathbf{F}_q}((t))$ is a subgroup of the absolute Galois group of $\mathbf{F}_q((t))$, and that we can say things about the former absolute Galois group.
May
21
comment Maximal separable extension of $\mathbb F_q((t))$
Three comments: first, $K^{sep}=L^{sep}$ where $L:=\overline{\mathbf{F}_q}((t))$. Second, every finite Galois extension of $L$ is totally ramified, with Galois group being a semidirect product of a normal $p$-subgroup by a cyclic prime-to-$p$ subgroup. Third, such semidirect products do not correspond to composita of field in the way you suggest, since your condition forces the group to be a direct product rather than a semidirect product.
May
21
revised Automorphism group of an affine curve
Fixed a previously wrong answer
May
21
revised Automorphism group of an affine curve
Fixed a previously wrong answer
May
21
revised Automorphism group of an affine curve
Corrected a mistake
May
21
answered Automorphism group of an affine curve
May
20
revised Is $x^p-x+1$ always irreducible in $F_p[x]$?
added 2 characters in body
May
20
revised Is $x^p-x+1$ always irreducible in $F_p[x]$?
added 2787 characters in body
May
20
awarded  Nice Answer